Explanation Given Information: The polynomial: x 2 n + 2 x n + 3 x n + 6 Concept Used: The GCF (Greatest Common Factor) of a list of integers is the largest integer that is a factor of all the integers in the list. The GCF (Greatest Common Factor) of a list of common variable factors raised to powers is the variable raised to the smallest exponent in the list. Distributive property: a ( b + c ) = a ⋅ b + a ⋅ c To factor the given four-term polynomial by grouping, first we will form two groups by taking the first two and last two terms. Then we factor out GCF from each group by rewriting each term of the group as a product of prime factors and identify the largest factor that is common in all terms. Then we factor out the GCF from each group by writing each term as a product of the GCF and the term’s remaining factors inside a parenthesis. In the given four-term polynomial, we can see that the GCF of first two terms is x n and the GCF of the last two terms is 3 .So we factor out these GCF’s from each group and rewrite the groups in factored form. So we get x 2 n + 2 x n + 3 x n + 6 = ( x 2 n + 2 x n ) + ( 3 x n + 6 ) = ( x n ⋅ x n + x n ⋅ 2 ) + (

15th Edition

ISBN: 9780321978929

Author: Martin-Gay

Publisher: PEARSON

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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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Chapter 13.1, Problem 115ES

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Factor the polynomial, x2n+2xn+3xn+6 by grouping.

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Chapter 13.1, Problem 114ES

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Factor the polynomial, x 2 n + 2 x n + 3 x n + 6 by grouping.

Solution Summary: The author explains how to factor a four-term polynomial by grouping.

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Factor the polynomial, x2n+2xn+3xn+6 by grouping.

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Chapter 13 Solutions