College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5: 123

Answer

Process to find GCF of the polynomial follow following steps 1. Break the every term of polynomial into prime factors. 2. Look for factors that appear common in every single term to determine the GCF. 3. Multiplication of the common factors results in GCF

Work Step by Step

Example- Let us consider a polynomial 6$x^{2}$ + $14x y^{2}$ - 42$xy$ -2$x^{2}y^{2}$ For finding the GCF of the polynomial we follow following steps 1. Break the every term of polynomial into prime factors. 6$x^{2}$ = 2$\times$3$\times$$x$$\times$$x$. $14x y^{2}$ = 2$\times$7$\times$$x$$\times$$y$$\times$$y$. 42$xy$ = 2$\times$3$\times$7$\times$$x$$\times$$y$. 2$x^{2}y^{2}$ = 2$\times$$x$$\times$$x$$\times$$y$$\times$$y$. 2. Look for factors that appear common in every single term to determine the GCF. Common factors = 2, $x$. 3. Multiplication of the common factors results in GCF So the GCF of given polynomial = 2$x$.
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