College Algebra (6th Edition)

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$$x. 14x y^{2} = 2\times7\times$$x$$\times$$y$$\times$$y$. 42$xy$ = 2$\times$3$\times$7$\times$$x$$\times$$y. 2x^{2}y^{2} = 2\times$$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$x$.