Explanation Formula used: If l, m, and n are two solution for the quadratic equation , then the quadratic is ( x − l ) ( x − m ) = 0 . Calculation: The solution set for the polynomial equation is [ − 4 , 3 ] ∪ [ 7 , ∞ ) . The intervals formed by the points − 4 , 3 , and 7 are ( − ∞ , − 4 ) , ( − 4 , 3 ) , ( 3 , 7 ) and ( 7 , ∞ ) . By using the formula, the polynomial equation is ( x + 4 ) ( x − 3 ) ( x − 7 ) = 0 , where l = − 4 , m = 3 and n = 7 . Simplify the above polynomial inequality as follows. ( x + 4 ) ( x − 3 ) ( x − 7 ) = 0 ( x 2 − 3 x + 4 x − 12 ) ( x − 7 ) = 0 ( x 2 + x − 12 ) ( x − 7 ) = 0 x 3 − 6 x 2 − 19 x + 84 = 0 Let the polynomial function is denoted by f ( x ) = x 3 − 6 x 2 − 19 x + 84 . Find the sign of the polynomial function by testing a point in each interval. Obtain the sign of the polynomial function f ( x ) = x 3 − 6 x 2 − 19 x + 84 at the point x = − 5 on an interval ( − ∞ , − 4 ) . f ( − 5 ) = ( − 5 ) 3 − 6 ( − 5 ) 2 − 19 ( − 5 ) + 84 = − 125 − 150 + 95 + 84 = − 96 < 0 Obtain the sign of the polynomial function f ( x ) = x 3 − 6 x 2 − 19 x + 84 at the point x = 0 on an interval ( − 4 , 3 )

Algebra and Trigonometry: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179049

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

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Chapter 4.6, Problem 94E

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To write: A polynomial inequality for the solution set [−4,3]∪[7,∞).

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Chapter 4.6, Problem 93E

Chapter 4.6, Problem 95E

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Chapter 4 Solutions

Algebra and Trigonometry: Graphs and Models (6th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 6E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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A polynomial inequality for the solution set [ − 4 , 3 ] ∪ [ 7 , ∞ ) .

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To write: A polynomial inequality for the solution set [−4,3]∪[7,∞).

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Chapter 4 Solutions