Answer
1. Determine the greatest common factor of all terms in the polynomial.
2. Express each term as the product of the GCF and its other factor.
3. Use the distributive property to factor out the GCF.
(see example in step-by-step)
Work Step by Step
Factoring a Monomial From a Polynomial
1. Determine the greatest common factor of all terms in the polynomial.
2. Express each term as the product of the GCF and its other factor.
3. Use the distributive property to factor out the GCF.
Example : $4x^{2}+10x^{3}+12x^{5},$
1. Determine the greatest common factor of all terms in the polynomial.
$2$ is a factor of all the coefficients,
$x^{2}$ is the smallest power of x that appears in all the terms,
So, the GCF is $2x^{2}.$
2. Express each term as the product of the GCF and its other factor.
$4x^{2}+10x^{3}+12x^{5}$ = $2x^{2}\cdot 2+2x^{2}\cdot 5x+2x^{2}\cdot 6x^{3}$
3. Use the distributive property to factor out the GCF.
... = $2x^{2}(2+5x+6x^{3})$
