Explanation Given Information: The provided polynomial is 2 x 3 − x 2 − 13 x − 6 . Formula used: Rational Zeros Theorem: If a polynomial ( a n x n + a n − 1 x n − 1 + ⋯ + a 1 x + a o ) has integer coefficient, then every rational zero is of the form x = p q , where p is a factor of a o , and q is a factor of a n . Calculation: Consider the polynomial, p ( x ) = 2 x 3 − x 2 − 13 x − 6 Factor of constant term ( − 6 ) of polynomial 2 x 3 − x 2 − 13 x − 6 will be ± 1 , ± 2 ± 3 and ± 6 . Factor of leading coefficient ( 2 ) will be ± 1 , ± 2 . Now apply, Rational Zeros Theorem for polynomial p ( x ) to find zeros. The possible rational zeros are the factor of the constant term divided by the factors of the leading coefficient that is, ± 1 , ± 1 2 , ± 1 3 , ± 3 2 , ± 2, ± 3 and ± 6 The possible rational factor of polynomial 2 x 3 − x 2 − 13 x − 6 is ± 1 , ± 1 2 , ± 1 3 , ± 3 2 , ± 2, ± 3 and ± 6 . Now, apply synthetic devisor method for x = 3 . 3 2 − 1 − 13 − 6 6 15 6 2 5 2 0 The factor of polynomial 2 x 3 − x 2 − 13 x − 6 are ( x − 3 ) ( 2 x 2 + 5 x + 2 ) . Consider the quadratic equation, 2 x 2 + 5 x + 2 Factor the quadratic equation 2 x 2 + 5 x + 2 , ( 2 x 2 + 5 x + 2 ) = 2 x 2 + 4 x + x + 2 = 2 x ( x + 2 ) + 1 ( x + 2 ) = ( x + 2 ) ( 2 x + 1 ) The factor of polynomial 2 x 3 − x 2 − 13 x − 6 are ( x − 3 ) ( x + 2 ) ( 2 x + 1 ) . To find zeros set first term of the factor ( x − 3 ) ( x + 2 ) ( 2 x + 1 ) equal to zero

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Chapter A4, Problem 70E

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Chapter A4, Problem 69E

Chapter A4, Problem 71E

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Chapter A4 Solutions

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Ch. A4 - Prob. 1CP Ch. A4 - Prob. 2CP Ch. A4 - Prob. 3CP Ch. A4 - Prob. 4CP Ch. A4 - Prob. 1E Ch. A4 - Prob. 2E Ch. A4 - Prob. 3E Ch. A4 - Prob. 4E Ch. A4 - Prob. 5E Ch. A4 - Prob. 6E

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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY

The factor the polynomial 2 x 3 − x 2 − 13 x − 6 .

Solution Summary: The author explains how to calculate the factor of the polynomial 2x3 — it's 3,-2, and-12

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Chapter A4 Solutions