Which is the completely factored form of 4x3 + 10x2 - 6x?

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

Step-by-step explanation:

Given

4x³ + 10x² - 6x (factor out 2x from each term)

= 2x (2x² + 5x - 3)

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x - term.

product = 2 * - 3 = - 6 and sum = + 5

The factors are + 6 and - 1

Use these factors to split the x - term

2x² + 6x - x - 3 (factor the first/second and third/fourth terms)

2x (x + 3) - 1 (x + 3) ← factor out (x + 3) from each term

(x + 3) (2x - 1), hence

2x² + 5x - 3 = (x + 3) (2x - 1)

Hence

4x³ + 10x² - 6x = 2x (x + 3) (2x - 1)