Question

factor the expression completely. -3 + 3x^5

Explanation:

Step1: Rearrange terms

$3x^5 - 3$

Step2: Factor out GCF

$3(x^5 - 1)$

Step3: Apply difference of fifth powers

Recall $a^5 - b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)$. Here $a=x, b=1$:
$3(x - 1)(x^4 + x^3 + x^2 + x + 1)$

Answer:

$3(x - 1)(x^4 + x^3 + x^2 + x + 1)$