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

Calculus: An Applied Approach (MindTap Course List)

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

Ch. A4 - Prob. 7E Ch. A4 - Prob. 8E Ch. A4 - Prob. 9E Ch. A4 - Prob. 10E Ch. A4 - Prob. 11E Ch. A4 - Prob. 12E Ch. A4 - Prob. 13E Ch. A4 - Prob. 14E Ch. A4 - Prob. 15E Ch. A4 - Prob. 16E Ch. A4 - Factoring Polynomials In Exercises 9-18, write the...Ch. A4 - Prob. 18E Ch. A4 - Prob. 19E Ch. A4 - Prob. 20E Ch. A4 - Prob. 21E Ch. A4 - Prob. 22E Ch. A4 - Prob. 23E Ch. A4 - Prob. 24E Ch. A4 - Prob. 25E Ch. A4 - Prob. 26E Ch. A4 - Prob. 27E Ch. A4 - Prob. 28E Ch. A4 - Prob. 29E Ch. A4 - Prob. 30E Ch. A4 - Prob. 31E Ch. A4 - Prob. 32E Ch. A4 - Prob. 33E Ch. A4 - Prob. 34E Ch. A4 - Prob. 35E Ch. A4 - Prob. 36E Ch. A4 - Prob. 37E Ch. A4 - Prob. 38E Ch. A4 - Prob. 39E Ch. A4 - Prob. 40E Ch. A4 - Prob. 41E Ch. A4 - Prob. 42E Ch. A4 - Prob. 43E Ch. A4 - Prob. 44E Ch. A4 - Prob. 45E Ch. A4 - Prob. 46E Ch. A4 - Prob. 47E Ch. A4 - Prob. 48E Ch. A4 - Prob. 49E Ch. A4 - Prob. 50E Ch. A4 - Prob. 51E Ch. A4 - Prob. 52E Ch. A4 - Prob. 53E Ch. A4 - Prob. 54E Ch. A4 - Prob. 55E Ch. A4 - Prob. 56E Ch. A4 - Prob. 57E Ch. A4 - Prob. 58E Ch. A4 - Prob. 59E Ch. A4 - Prob. 60E Ch. A4 - Prob. 61E Ch. A4 - Prob. 62E Ch. A4 - Prob. 63E Ch. A4 - Prob. 64E Ch. A4 - Prob. 65E Ch. A4 - Prob. 66E Ch. A4 - Prob. 67E Ch. A4 - Prob. 68E Ch. A4 - Prob. 69E Ch. A4 - Prob. 70E Ch. A4 - Prob. 71E Ch. A4 - Prob. 72E Ch. A4 - Prob. 73E Ch. A4 - Prob. 74E Ch. A4 - Prob. 75E Ch. A4 - Prob. 76E

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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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To calculate: The factor the polynomial 2x3−x2−13x−6.

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Chapter A4 Solutions