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: 87



Work Step by Step

1. Determine the greatest common factor of all terms in the polynomial. $24=6\times 4,\quad 30=6\times 5,\quad 18=6\times 3,$ the greatest integer factor is $6.$ 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 $x^{2}yz .$ $GCF=6x^{2}yz .$ 2. Express each term as the product of the GCF and its other factor. $ \begin{array}{lll} 24x^{3}y^{3}z^{3} & +30x^{2}y^{2}z & +18x^{2}yz^{2}=\\ =6x^{2}yz\cdot 4xy^{2}z^{2} & +6x^{2}yz\cdot 5y & +6x^{2}yz\cdot 3z \end{array}$ 3. Use the distributive property to factor out the GCF. = $6x^{2}yz(4xy^{2}z^{2}+5y+3z)$
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