Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.1 - The Greatest Common Factor and Factoring by Grouping - Exercise Set - Page 427: 88


$8x^{2}yz (2yz+4z+3)$

Work Step by Step

1. Determine the greatest common factor of all terms in the polynomial. $16=8\times 2,\quad 32=8\times 4,\quad 24=8\times 3,$ the greatest integer factor is $8.$ The variable part of the greatest common factor always contains the smallest power of a variable that appears in all terms of the polynomial. Here, it is $x^{2}yz .$ $GCF=8x^{2}yz .$ 2. Express each term as the product of the GCF and its other factor. $ \begin{array}{lll} 16x^{2}y^{2}z^{2} & +32x^{2}yz^{2} & +24x^{2}yz=\\ =8x^{2}yz \cdot 2yz & +8x^{2}yz \cdot 4z & +8x^{2}yz \cdot 3 \end{array}$ 3. Use the distributive property to factor out the GCF. = $8x^{2}yz (2yz+4z+3)$
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