Explanation Given information: Graph of the polynomial touches the x − axis at x = 4 , crosses the x − axis at x = − 2 and x = 1 , and has a y − intercept of 4 Explanation: Graph of the polynomial touches the x − axis at x = 4 , that implies degree of x = 4 is 2 Graph of the polynomial crosses the x − axis at x = − 2 and x = 1 , thus both have degree 1 If r is a real zero of a polynomial function, then ( x − r ) is a factor of the function f ( x ) Hence, the factors of the polynomial function f ( x ) are ( x − 4 ) 2 , ( x + 2 ) and ( x − 1 ) By using these factors, the polynomial is in the form of f ( x ) = a ( x − 4 ) 2 ( x + 2 ) ( x − 1 ) , where a is a non-zero real number. Now, y − intercept of the graph of polynomial is 4 At y − intercept, x = 0 , thus substitute x = 0 , y = 4 in f ( x ) = a ( x − 4 ) 2 ( x + 2 ) ( x − 1 )

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ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 12.3, Problem 118AYU

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The factored form of the polynomial function of smallest degree that touches the x− axis at x=4, crosses the x− axis at x=−2 and x=1, and has a y− intercept of 4

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Chapter 12.3, Problem 117AYU

Chapter 12.3, Problem 119AYU

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The factored form of the polynomial function of smallest degree that touches the x − axis at x = 4 , crosses the x − axis at x = − 2 and x = 1 , and has a y − intercept of 4

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The factored form of the polynomial function of smallest degree that touches the x− axis at x=4, crosses the x− axis at x=−2 and x=1, and has a y− intercept of 4

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