Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-2 Multiplying and Factoring - Got It? - Page 493: 3


a. $\quad3x^{2}(3x^{4}+5x^{2}+4)$ b. $\quad-6x^{2}(x^{2}+3x+2)$

Work Step by Step

a. $ 9x^{6}+15x^{4}+12x^{2}\qquad$ factor the polynomial, first factor each term. $9x^{6}=(3)\cdot 3\cdot[x\cdot x]\cdot x\cdot x\cdot x\cdot x$ $15x^{4}=(3)\cdot 5\cdot[x\cdot x]\cdot x\cdot x$ $12x^{2}=2\cdot 2\cdot(3)\cdot[x\cdot x]$ GCF= $(3)\cdot[x\cdot x]$, or $3x^{2}$. $ 9x^{6}+15x^{4}+12x^{2}\qquad$ ...factor out the GCF from each term $=3x^{2}(3x^{4})+3x^{2}(5x^{2})+3x^{2}(4)\qquad$ ...apply the Distributive Property. $=3x^{2}(3x^{4}+5x^{2}+4)$ b. $-6x^{4}=(-1)\cdot(2)\cdot(3)\cdot(x\cdot x)\cdot x\cdot x$ $-18x^{3}=(-1)\cdot(2)\cdot(3)\cdot 3\cdot(x\cdot x)\cdot x$ $-12x^{2}=(-1)\cdot(2)\cdot 2\cdot(3)\cdot(x\cdot x)$ GCF=$(-1)\cdot(2)\cdot(3)\cdot(x\cdot x)$, or $-6x^{2}$. $-6x^{2}(x^{2}+3x+2)$
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