Answer:
(x - 1)(x - 3)(x + 2).
Explanation:
f(1) = 1^3 - 2(1)^2 - 5(1) + 6
= 1 - 2 - 5 + 6
= 0
so one factor is (x - 1) (by the Factor Theorem).
Divide f(x) by x - 1 we get:
x- 1) x^3 - 2x^2 - 5x + 6 ( x^2 - x - 6 <------ answer
x^3 - x^2
-x^2 - 5x
-x^2 + x
-6x + 6
-6x + 6
= x^2 - x - 6
= (x - 3)(x + 2).