Question

factor out the greatest common factor from the following polynomial.
$2x^6 - 8x^5 + 4x^4$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. $2x^6 - 8x^5 + 4x^4 = \square$ (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 2, -8, 4. The GCF of 2, 8, 4 is 2.

Step2: Find GCF of variables

For \(x^6\), \(x^5\), \(x^4\), the lowest power is \(x^4\). So GCF of variables is \(x^4\).

Step3: Factor out GCF

Factor out \(2x^4\) from \(2x^6 - 8x^5 + 4x^4\):
\(2x^4(x^2 - 4x + 2)\)

Answer:

\(2x^4(x^2 - 4x + 2)\) (So the correct choice is A with this factored form)