Question

which product of prime polynomials is equivalent to $30x^3 - 5x^2 - 60x$?
$x(10x + 3)(3x - 4)$
$5x(2x - 3)(3x + 4)$
$5x(2x + 3)(3x - 4)$
$5(2x^2 - 3)(3x + 4)$

Explanation:

Step1: Factor out GCF

$30x^3 - 5x^2 - 60x = 5x(6x^2 - x - 12)$

Step2: Factor quadratic trinomial

Find two numbers: $8$ and $-9$, since $8 \times (-9) = -72$ and $8 + (-9) = -1$.
Rewrite and group:
$6x^2 + 8x - 9x - 12 = 2x(3x + 4) - 3(3x + 4) = (2x - 3)(3x + 4)$

Step3: Combine factors

$5x(6x^2 - x - 12) = 5x(2x - 3)(3x + 4)$

Answer:

$5x(2x - 3)(3x + 4)$