Question

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)

Answer 1

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

Answer 2

Answer: 3x(x-3)(x-5)

Explanation:

The negative has to be consistance because of the earlier factoring