Question

Factor the greatest common factor out of 8x^3 + 28x^2 + 40x

Answer 1

Answer: $4x(2x^2+7x+10)$

Step-by-step explanation:

The Greatest Common Factor (GCF) of a polynomial is defined  as the largest monomial that is a factor of all the terms of the polynomial.

In this case, given this polynomial:

$8x^3 + 28x^2 + 40x$

You can factor out the Greatest Common Factor applying this procedure:

1. Write the terms of the polynomial in prime factor form:

$8x^3=2*2*2*x*x*x\\\\28x^2=2*2*7*x*x\\\\40x=2*2*2*5*x$

2. Identify the factors the terms have in common (this will be the Greatest Common Factor). In this case this is:

$GCF=2*2*x=4x$

3. Finally,  rewrite the expression in factor form:

$4x(2x^2+7x+10)$

Answer 2

Answer:

4x

Step-by-step explanation:

When you divide the #'s by 4x you get an expression that cannot be divided any further.