Question

completely factor this polynomial. do not use the space bar when typing your answers.
(3x^3 - 27x)
factored form =

Explanation:

Step1: Factor out GCF

Factor out $3x$ from the polynomial.
$3x^3 - 27x = 3x(x^2 - 9)$

Step2: Factor difference of squares

Rewrite $x^2 - 9$ as a difference of squares and factor.
$x^2 - 9 = x^2 - 3^2 = (x+3)(x-3)$

Step3: Combine factors

Substitute the factored form back into the expression.
$3x(x^2 - 9) = 3x(x+3)(x-3)$

Answer:

$3x(x+3)(x-3)$