Factoring polynomials?

Question

I've got this problem: 24x^3+40x^2-54x-90 I got as far as 2(12x^3+20x^2-27x-45) and I don't know how to proceed. Help please? I think these problems get harder as I go, so if there's a basic step-by-step for factoring polynomials, that'd be nice to know about too.

Answer 1

24x ³ + 40x ² - 54x  - 90

= 2 (12x ³ + 20x ² - 27x - 45)

= 2 [4x ²(3x + 5) - 9 (3x + 5)]

= 2 [(3x + 5)(4x ² - 9)]

= 2 [(3x + 5)((2x )² - 3² )]

(a - b )² = (a - b )(a + b )

a = 2x  , b = 3

= 2(3x + 5)(2x + 3)(2x - 3)

Factoring of 24x ³ + 40x ² - 54x  - 90 = 2(2x - 3) (2x  + 3 )(3x  + 5 ).