What is the factorization of the trinomial below 3x^3-24x^2+45x

A. 3 (x-3) (x+5)

B. 3 (x^2-3) (x+5)

C. 3x (x-3) (x-5)

D. 3x (x-3) (x-5)

1st factor is 3x:

= 3x (x² - 8x + 15)

2nd & 3rd factors:

x² - 8x + 15 = 0

x² - 4x = - 15 + ( - 4) ²

x² - 4x = - 15 + 16

(x - 4) ² = 1

x - 4 = 1

= x - 4 - 1, = x - 5

= x - 4 + 1, = x - 3

Answer: 3x (x - 5) (x - 3) are the factors.

Proof:

= 3x (x - 5) (x - 3)

= 3x (x² - 5x - 3x + 15)

= 3x (x² - 8x + 15)

= 3x³ - 24x² + 45x