Answer:
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)
