Algebra & Trigonometry (10th Edition)
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The vertex is .The axis of the parabola is the ... more
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The vertex is .The intercepts are and . ; The ... more
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The standard form of the quadratic function is ; ... more
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The maximum height of the baseball is . ; A ... more
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Polynomial ; Every linear, constant, and squaring ... more
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Non-negative integer ; According to the definition... more
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Quadratic ; A quadratic function is of the form ... more
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Negative, Maxima ; When the graph of a quadratic ... more
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It can be that the vertex of the graph is at . ... more
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intercepts: Axis of symmetry: ; The standard form ... more
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intercept: ,Axis of symmetry: ; The standard ... more
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intercept: Axis of symmetry: ; The standard form ... more
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intercepts: Axis of symmetry: ; The standard ... more
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,Axis of symmetry: intercepts: and . ; The ... more
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Axis of symmetry: No intercept. ; The function ... more
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Axis of symmetry: No intercept. ; The standard ... more
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Axis of symmetry: No intercept. ; The standard ... more
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Axis of symmetry: intercepts: and ; The ... more
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Axis of symmetry: intercepts: and ; The standard ... more
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; The standard form of the function is . ; Let ... more
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Vertex is ( 0.25, 0.875)Axis of symmetry is x=0.... more
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The expression of the function in its standard ... more
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The expression of the function in its standard ... more
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The given quadratic equation is, f(x)=x2+10x+14The... more
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(Graphed using desmos.com)f(x) = -2x2 + 12x - 18 ... more
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The expression of the function in its standard ... more
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; Since the vertex is , the equation of the ... more
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; Since the vertex is , the equation of parabola ... more
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; Since the vertex is , the equation of parabola ... more
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; Since the vertex is , the equation of parabola ... more
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; Since the vertex is , the equation of parabola ... more
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; Since the vertex is , the equation of parabola ... more
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; Since the vertex is , the equation of parabola ... more
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; Since the vertex is , the equation of parabola ... more
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; Since the vertex is , the equation of parabola ... more
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; Express the generalized standard description of... more
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; Express the generalized standard description of... more
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; Express the generalized standard description of... more
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and ; Sketch the parabola that represents the ... more
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and ; Equate the first factor to and solve for ... more
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and ; Sketch the parabola that represents the ... more
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and ; Sketch the parabola that represents the ... more
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and same ; Sketch the parabola that represents ... more
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and same ; Sketch the parabola that represents ... more
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Sketch the parabola that represents the quadratic ... more
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and same ; Sketch the parabola that represents ... more
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and same ; Sketch the parabola that represents ... more
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and ; Write the expression of a quadratic ... more
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and ; Write the expression of a quadratic ... more
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and ; Write the expression of a quadratic ... more
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and ; Write the expression of a quadratic ... more
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and ; Write the expression of a quadratic ... more
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and ; Write the expression of a quadratic ... more
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55 and 55 ; Assume and to be two real positive ... more
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S/2 S/2 ; Assume x1 and x2 to be two real positive... more
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126 ; Assume and be two real positive numbers ... more
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217 ; Assume and be two real positive numbers ... more
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; is a quadratic equation of .Compare with the ... more
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20 units ; or is a quadratic equation of x .... more
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; or is a quadratic equation of .Compare with ... more
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True ; At the intercept, . For in , has no real... more
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TrueThe axis of symmetry of the graph of both the ... more
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; is a quadratic equation of .Compare it with ... more
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. ; Write the function in the standard form of a ... more
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The vertex is . ; Write the function in the ... more
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The two roots of the function are and .Find the ... more
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, .3 ; Find the zeros of the function by solving ... more
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The degree of is odd, and the leading coefficient... more
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The degree of is even, and the leading ... more
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. ; Find the values of the function for some ... more
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continuous. ; The polynomial function has no point... more
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Leading Coefficient Test. ; Let .If the degree of... more
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. ; A polynomial function can have a maximum ... more
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touches ; As the function is of even multiplicity... more
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repeated zero ; The zero of a function is the ... more
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standard ; The standard form of the equation ... more
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Intermediate value ; According to the intermediate... more
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is the equation of a parabola. So, graph (e) is ... more
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The graph will fall on the left-hand side and rise... more
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The graph will rise from the left-hand side and ... more
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The graph will fall on the left-hand side and ... more
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The graph will fall on the left-hand side and ... more
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The graph will rise on the left-hand side and fall... more
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The graph will fall on the left-hand side and rise... more
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The graph will rise on the left-hand side, and ... more
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The graph will rise on the left-hand side and fall... more
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The graph will rise on the left-hand side and fall... more
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The graph will fall on the left-hand side and ... more
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The leading coefficient is positive, and the ... more
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The leading coefficient is negative, and the ... more
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The leading coefficient is negative, and the ... more
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The graphs are plotted using the zeros of ... more
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. ; The polynomial function with zeroes and is ... more
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. ; The polynomial function with zeroes and is ... more
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. ; The polynomial function with zeroes and is ... more
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. ; The polynomial function with zeroes and is ... more
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. ; The polynomial function with zeroes and is ... more
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. ; The polynomial function with zeroes and is ... more
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. ; The polynomial function with zeroes and is ... more
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. ; The polynomial function with zeroes and is ... more
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. ; The polynomial function with zeroes and is ... more
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. ; The polynomial function with zeroes and is ... more
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. ; Polynomial of degree 2 with the zeroes and ... more
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. ; Polynomial of degree 2 with the zeroes and ... more
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. ; Polynomial of degree 3 with the zero and is ... more
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. ; Polynomial of degree 3 with the zero and is ... more
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. ; Polynomial of degree 4 with the zero and is ... more
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. ; Polynomial of degree 4 with the zero and is ... more
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. ; A polynomial function has repeated zeros at ... more
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. ; A polynomial function has repeated zeros at ... more
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Zeros: 0,-4,4.Odd multiplicity. ; Graph the ... more
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Zeros: 0,-2.83, 2.83.Even multiplicity: 0.Odd ... more
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Zeros: .Even multiplicity: .Odd multiplicity: 3 ... more
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Zeros: -2, , even multiplicity. ; Graph the ... more
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200. ; The point on the graph at which the ... more
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The leading coefficient of a polynomial function ... more
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A polynomial of degree has a maximum of turning ... more
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Because the graph of the polynomial function with ... more
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For the polynomial function , if the degree of the... more
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The graph of a fourth degree polynomial function ... more
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The graph of a fifth degree polynomial function ... more
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. ; Divide the polynomial by the expression by ... more
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. ; Since the coefficient of is 0, rewrite the ... more
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.Check part:. ; Rewrite the term of the dividend ... more
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. ; Arrange the coefficient of the polynomial in ... more
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Apply the synthetic division method to divide the ... more
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is dividend. is divisor. is quotient. is ... more
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Proper. ; The rational expression is said to be ... more
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Improper. ; If the degree of the numerator is ... more
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synthetic. ; The synthetic division method is used... more
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Factor. ; Write the condition when the function ... more
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Remainder. ; Write the condition when the function... more
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Divide the dividend by the divisor with the help... more
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Divide the dividend by the divisor with the help... more
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; Divide the function by the function with the ... more
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for . ; Divide the function by the function ... more
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; Divide the function by the function with the ... more
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; Divide the function by the function with the ... more
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; Divide the function by the function with the ... more
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; Divide the function by the function with the ... more
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; Divide the function by the function with the ... more
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; Divide the function by the function with the ... more
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; Divide the function by the function with the ... more
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; Divide the function by the function with the ... more
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; Rearrange the polynomial to convert it into a ... more
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; Rearrange the polynomial to convert it into a ... more
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; Apply the property of formula to expand the ... more
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; Apply the formula to expand the denominator ... more
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; As is the zero of the divisor , set 4 in the ... more
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, for . ; As is the zero of the divisor , set -3 ... more
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, for ; As is the zero of the divisor , set 3 in ... more
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, for ; As is the zero of the divisor , set -4 in... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; The coefficients in order from the highest to ... more
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; Dividing the function with by synthetic ... more
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; Dividing the function with by synthetic ... more
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; Dividing the function with by synthetic ... more
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; Dividing the function with by synthetic ... more
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.. ; Find the quotient and remainder using ... more
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; As is the zero of the divisor, set it in the ... more
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is solution to the given polynomial as the ... more
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is a solution of the given polynomial as the ... more
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Synthetic division is used to verify that the ... more
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Synthetic division is used to verify that the ... more
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Synthetic division is used to verify that the ... more
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Synthetic division is used to verify that the ... more
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Synthetic division is used to verify that the ... more
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Synthetic division is used to verify that the ... more
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, where . ; To simplify the expression, use the ... more
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; To simplify the expression, use the long ... more
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, where . ; To simplify the expression, use the ... more
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, where . ; Use the long division method and the ... more
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False; will be the zero of . ; To find the zero ... more
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True;Equate the factor of to zero and obtain . ... more
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False;The total degree of the numerator is greater... more
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False;The equation is not true for . ; At , the ... more
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, where . ; To simplify the expression, use the ... more
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; more
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-210 ; is divided by evenly. Thus, is a factor ... more
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42 ; is divided by evenly. Thus, is a factor of... more
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7 ; According to the factor theorem, is a factor ... more
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4. ; As the degree of the polynomial function is... more
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No rational zeros. ; The leading coefficient and ... more
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5,5,5. ; The leading coefficient and the constant ... more
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2,-3, ; Identify the leading term coefficient and ... more
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-1, -3.84, and 2.34. ; Identify the leading term ... more
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. ; The zeros of the polynomial are 2, -2, and . ... more
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. ; The zeros of the polynomial are and . Since ... more
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. ; One of the zeros of the polynomial is . Since ... more
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. ; Since the leading term coefficient is 1 and ... more
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The polynomial has no real positive roots.It has ... more
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and ; The polynomial has 3 variations in signs. ... more
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; Assume that the length of each side of the base... more
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fundamental. ; The fundamental theorem of algebra... more
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linear ; The linear factorization theorem states ... more
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Rational. ; The rational zeros of a polynomial ... more
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Complex. ; For any polynomial that has real ... more
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Linear. ; Every polynomial of degree can be ... more
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irreducible. ; Any quadratic equation that cannot ... more
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Descartes. ; Descartes rule of signs states that ... more
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lower. ; If all the real zeros of a polynomial ... more
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3. ; The degree of the polynomial is 3.Therefore... more
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4. ; The degree of the polynomial function is ... more
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5. ; The degree of the polynomial function is ... more
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6. ; The degree of the polynomial function is six... more
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2. ; The degree of the polynomial function is 2. ... more
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1 ; Expanding the polynomial function,The degree ... more
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Contained in the list. ; When the leading ... more
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Contained. ; When the leading coefficient of a ... more
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Contained. ; When the leading coefficient of a ... more
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Contained. ; When the leading coefficient of a ... more
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-1, -2, 3. ; In the polynomial function , the ... more
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. ; In the polynomial function , the leading ... more
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No rational zeros. ; In the polynomial function , ... more
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-5,2,3 ; Possible rational zeroes for a polynomial... more
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-6,-1. ; The polynomial has a leading coefficient... more
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No rational zero. ; The polynomial has a leading ... more
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. ; Possible rational zeroes for a polynomial are... more
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No rational zero. ; Possible rational zeros for a ... more
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. ; Possible rational zeros for a polynomial are ... more
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. ; Possible rational zeroes for a polynomial are... more
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. ; Possible rational zeroes for a polynomial are... more
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. ; Possible rational zeroes for a polynomial are ... more
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. ; Possible rational zeros for a polynomial are ... more
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. ; Possible rational zeros for a polynomial are ... more
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. ; is a zero of , and the polynomial has real ... more
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. ; - is a zero of , and the polynomial has real ... more
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. ; is a zero of , and the polynomial has real ... more
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. ; is a zero of and the polynomial has real ... more
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. ; is a zero of , and the polynomial has real ... more
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. ; is a zero of and the polynomial has real ... more
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. ; is a zero of , and the polynomial has real ... more
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. ; is a zero of , and the polynomial has real ... more
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. ; is a zero of , and the polynomial has real ... more
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. ; is a zero of , and the polynomial has real ... more
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. ; Complex zeros occur in conjugate pairs. Thus... more
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. ; Complex zeros occur in conjugate pairs. Thus... more
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. ; Complex zeros occur in conjugate pairs. Thus... more
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. ; Complex zeros occur in conjugate pairs. Thus... more
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. ; Complex zeros occur in conjugate pairs. Thus... more
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. ; Complex zeros occur in conjugate pairs.Since... more
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Zeroes of the function: . ; The polynomial is ... more
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,Zeros of the function: . ; The polynomial is ... more
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Zeros of the function: . ; The polynomial is ... more
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Zeros of the function: . ; The polynomial is ... more
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; Zeros of the function: ; The function is ... more
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The zeros are . ; For the polynomial , the leading... more
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The zeros are . ; The rational zeros of are . ... more
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The zeros are . ; In the polynomial , the leading ... more
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The roots are -1, , and . ; Since the leading term... more
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The roots are -3, , and . ; Since the leading term... more
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The roots are 2, and. ; In the polynomial , the ... more
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The roots are -3 and . ; The leading term ... more
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The zeros are -10,, and . ; Since the leading ... more
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The zeros are and . ; The coefficient of the ... more
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and . ; The leading term coefficient of the ... more
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1, and . ; The leading term coefficient of the ... more
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The zeros are and . ; In the polynomial , the ... more
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2, and . ; Since the leading term of the ... more
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Positive real zeroes: 1.Negative real zeroes: 0... more
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Positive real zeros: 2 or 0.Negative real zero: 0... more
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Positive real zero: 0.Negative real zero: 1. ; ... more
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Positive real zeroes: 1.Negative real zeroes: 0 or... more
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Positive real zeros: 0 or 2.Negative real zeros: 0... more
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Positive real zeroes: 1.Negative real zeroes: 0 or... more
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Positive real zeroes: 0 or 2. Negative real zeroes... more
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Positive real zeroes: 0 or 2.Negative real zeroes... more
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, and . ; Set the given as equal to zero, and ... more
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, and . ; Set the given as equal to zero, and ... more
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. ; Set the given function as equal to zero, and ... more
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; Set the given as equal to zero, and factor the... more
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-2, , and 2. ; Set the given function as equal ... more
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-3, and 4. ; In the given function , the leading ... more
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-1, and 1. ; Set the given function as equal to ... more
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-2, and . ; In the given function , the leading ... more
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Substitute 0 for in the function and solve it ... more
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4,000 units. ; It is possible to solve this ... more
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False;It is observed that the third-degree ... more
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True;It is observed that complex roots or ... more
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. ; Obtain the relationship between and . ; . ; ... more
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. ; The function has zeros at .Obtain the ... more
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. ; The function has zeros at .Obtain the ... more
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. ; The function has zeros at .Obtain the ... more
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The zeros cannot be determined. ; It cannot be ... more
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. ; The function has zeros at .Obtain the ... more
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. ; Infinitely many functions are possible. ; It ... more
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. ; It is given that the function has a zero at ... more
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; It can be observed that the graph of crosses ... more
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; It can be observed that the graph crosses the... more
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The fourth factor of the function is missing, so ... more
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; The complex zeros of a function always occur in... more
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; The complex zeros of a function always occur in... more
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Insert the function in the graphing utility to ... more
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Consider for the year 2008.Substitute the given ... more
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. ; Consider as the constant of proportionality, ... more
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. ; Consider as the constant of proportionality; ... more
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Approximately . ; Considering to be the constant ... more
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Approximately . ; Consider to be the constant of ... more
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. ; Consider to be the constant of ... more
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variation ; Write the techniques which are ... more
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sum. ; Sum of the square difference method is a ... more
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least. ; There is always a slight difference ... more
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correlation. ; The value lies between , and is a ... more
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directly proportional. ; Consider the function . ... more
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inverse. ; Consider the function .Substitute in ... more
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combined. ; Consider the function . Substitute ... more
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jointly proportional. ; Consider the function . ... more
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; Sketch a graph of the line that best ... more
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; Sketch a graph of the line that best ... more
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; Sketch a graph of the line that best ... more
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. ; Sketch a graph of the line that best ... more
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; Sketch a graph of the line that best ... more
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; Sketch a graph of the line that best ... more
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. ; For direct variation, differs directly as or... more
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. ; For direct variation, differs directly as or... more
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. ; For direct variation, differs directly as or... more
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. ; For direct variation, differs directly as or... more
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. ; For direct variation between and , it can be ... more
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. ; For direct variation between and , differs ... more
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2468104163664100 ; The expression for the ... more
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24681083272128200 ; The expression for the ... more
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246810432108256500 ; The expression for the ... more
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24681021654128250 ; The expression for the ... more
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2468101 ; The expression for the direction inverse... more
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246810 ; The expression for the direction inverse ... more
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246810 ; The expression for the direction inverse ... more
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2468105 ; The expression for the direction inverse... more
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varies inversely with respect to . ; It can be ... more
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Direct variation ; It can be observed from the ... more
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. ; According to the direct variation , the ... more
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. ; In direct variation , the ratio of any two ... more
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. ; In direct variation , the ratio of any two ... more
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. ; In direct variation , the ratio of any two ... more
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; It is given that variable varies directly with... more
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; It is given that the variable varies directly ... more
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; It is given that the variable varies inversely... more
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; An inverse variation is defined as varies in ... more
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; The relation for direct variation between and... more
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; If a variable is in direct variation with as ... more
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; A direction variation of with respect to is ... more
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; The expression for the direction inverse ... more
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; The expression for the direction variation ... more
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; It is given that the gravitational force of ... more
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is directly proportional to the square of . ; The... more
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is inversely proportional to . ; The expression ... more
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is jointly proportional to and . ; The ... more
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is jointly proportional to and the square of... more
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. ; It is known that varies directly with , which... more
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. ; It is known that varies directly with , which... more
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. ; It is known that varies inversely with . This... more
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. ; Let the proportional constant be . The model ... more
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. ; Let the proportional constant be . The model ... more
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. ; Let the proportional constant be . The model ... more
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. ; Let the proportional constant be . The model ... more
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. ; Let the proportional constant be . The model ... more
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. ; Let the proportional constant be . The model ... more
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. ; Let the proportional constant be . The model ... more
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; and . ; Let the proportional constant be . The ... more
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;; and . ; Let the proportional constant be . The ... more
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. ; Let the proportional constant be . The model ... more
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. ; Let the proportional constant be . The model ... more
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. ; The length of the spring equals to half the ... more
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. ; Let the proportional constant be . The model ... more
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. ; Let the proportional constant be . The model ... more
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If is directly proportional to and the variable... more
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If the variable is inversely proportional to to ... more
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is a constant not a variable. So, the surface ... more
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; Substitute in the equation to find the ... more
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; ; Vertex:, Axis of symmetry: ;-intercepts... more
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Given:f(x)=x2−6x+1 Required:standard form, graph, ... more
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. ; Vertex:;Axis of symmetry: ;-intercepts: , . ; ... more
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. ; Vertex:;Axis of symmetry: ;-intercepts: , . ; ... more
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; Vertex:;Axis of symmetry: ;-intercepts: , ; The... more
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. ; Vertex:;Axis of symmetry: ;No -intercepts. ; ... more
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. ; Vertex:;Axis of symmetry: ;-intercepts: , . ; ... more
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Focus (2,2)Deritrix y=3(x-h)2 = 4p(y-k)center (h,k... more
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1091. ; By leading coefficient test, the equation... more
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Since is even, the graph of will be similar to ... more
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Since is odd, the graph of will be similar to ... more
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Falls to the left and to the right. ; .The sign of... more
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Rises to the left and falls to the right. ; The ... more
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Falls to the left and rises to the right. ; The ... more
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Rises to the left and to the right. ; Here, .The ... more
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; Divide the expression by using the long ... more
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; The factor theorem states that:Use long ... more
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; The coefficients of the expression are 2, -25... more
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2. ; Determine the degree and type of the given ... more
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5. ; Determine the degree and type of the given ... more
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. ; Find one of the zeros of the polynomial by ... more
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. ; Find one of the zeros of the polynomial by ... more
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. ; Find one of the zeros of the polynomial by ... more
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. ; The linear factor form of degree polynomial ... more
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3 or 1 positive.2 negative. ; For the positive ... more
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SOLUTIONAnalysis of the question above is as shown... more
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; Find the equation relating the average travel ... more
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; Find the equation relating the average travel ... more
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Answer: more
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; To find the parabola equation, substitute the ... more
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It rises to the left and falls to the right. ; ... more
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; To divide by , using the long division, divide... more
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; Write in synthetic division format, carry down ... more
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and . ; Write in synthetic division format, ... more
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we can use the Rational Root Theorem. This theorem... more
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; If is the constant of proportionality, the ... more
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; Express the relation between , and using the ... more
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; Express the relation between and with as the... more
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Proof:Divide by using the division algorithm and ... more
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Not possible ; According to Descartes rule of ... more
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Check for the degree of the given polynomial ... more
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Let's assume that the length of each side of the ... more