Step-by-step explanation:
x³ - x² - 24x - 36
factors of -36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and negative equivalents.
1 - 1 - 24 - 36 != 0
8 - 4 - 48 - 36 != 0
27 - 9 - 72 - 36 != 0
64 - 16 - 96 - 36 != 0
216 - 36 - 144 - 36 = 0
So one factor is 6
x = 6
(x - 6) = 0
x²(x - 6) = x³ - 6x²
5x(x - 6) = 5x² - 30x
6(x - 6) = 6x - 36
x³ - 6x² + 5x² - 30x + 6x - 36
(x - 6)(x² + 5x + 6)
(x - 6)(x² + 3x + 2x + 6)
(x - 6)(x(x + 3) + 2(x + 3))
(x - 6)(x + 3)(x + 2)
x - 6 = 0
x = 6
x + 3 = 0
x = -3
x + 2 = 0
x = -2
x = -2, -3, 6.
One is the product of the other 2 as -2 x -3 = 6.
Graphic proof is shown above or below in the image
