Question

factor out the greatest common factor from the following polynomial.
$6x^5 - 48x^4 + 18x^3$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. $6x^5 - 48x^4 + 18x^3 = \square$ (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 6, -48, 18.
GCF of 6, 48, 18 is 6.

Step2: Find GCF of variable terms

The variable terms are $x^5$, $x^4$, $x^3$.
GCF is $x^3$ (lowest exponent).

Step3: Factor out overall GCF

Factor $6x^3$ from each term:
$6x^5 - 48x^4 + 18x^3 = 6x^3(x^2 - 8x + 3)$

Answer:

A. $6x^5 - 48x^4 + 18x^3 = 6x^3(x^2 - 8x + 3)$ (Type your answer in factored form.)