Question

Use the rational root theorem and synthetic division to factor x^3 + 2x^2 – 5x – 6.

(x + 3)(x – 2)(x – 1)

(x – 3)(x + 2)(x – 1)

(x + 3)(x – 2)(x + 1)

Answer 1

Possible rational roots: ±1, ±2, ±3, ±6. Test x = -1:
f(-1) = (-1)^3 + 2(-1)^2 – 5(-1) – 6 = -1 + 2 + 5 - 6 = 0, so x = -1 is a root.

Synthetic division by -1:
Coefficients: 1 2 -5 -6
Bring down 1 → multiply -1 → -1 → add to 2 → 1 → multiply -1 → -1 → add to -5 → -6 → multiply -1 → 6 → add to -6 → 0

Quotient is x^2 + x - 6, which factors as (x + 3)(x - 2). Therefore
x^3 + 2x^2 – 5x – 6 = (x + 3)(x - 2)(x + 1).

So the correct choice is: (x + 3)(x – 2)(x + 1).