Question

which is the completely factored form of $4x^3 + 10x^2 - 6x$?
$2(x - 3)(2x + 1)$
$2(x + 3)(2x - 1)$
$2x(x - 3)(2x - 1)$
$2x(x + 3)(2x - 1)$

Explanation:

Step1: Factor out GCF

$4x^3 + 10x^2 - 6x = 2x(2x^2 + 5x - 3)$

Step2: Factor quadratic trinomial

Find two numbers: $6$ and $-1$, since $6 \times (-1) = -6$ and $6 + (-1) = 5$.
$2x^2 + 5x - 3 = 2x^2 + 6x - x - 3 = 2x(x+3) -1(x+3) = (x+3)(2x-1)$

Step3: Combine factors

$2x(2x^2 + 5x - 3) = 2x(x+3)(2x-1)$

Answer:

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