Question

factor out the greatest common factor from the following polynomial.
$5x^6 - 40x^5 + 20x^4$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. $5x^6 - 40x^5 + 20x^4 = \square$ (type your answer in factored form.)
b. the polynomial has no common factor other than 1.

Explanation:

Step1: Find GCF of coefficients

The coefficients are 5, -40, 20. The greatest common factor is 5.

Step2: Find GCF of variable terms

The variable terms are $x^6$, $x^5$, $x^4$. The greatest common factor is $x^4$.

Step3: Factor out overall GCF

Factor $5x^4$ from each term of the polynomial:
$5x^6 - 40x^5 + 20x^4 = 5x^4(x^2) + 5x^4(-8x) + 5x^4(4)$
Simplify to get the factored form: $5x^4(x^2 - 8x + 4)$

Answer:

A. $5x^6 - 40x^5 + 20x^4 = 5x^4(x^2 - 8x + 4)$ (Type your answer in factored form.)