Question

The polynomial x3 + 4x2 – 9x – 36 has 4 terms. Use factoring by grouping to find the correct factorization.

(x2 + 9)(x + 4)

(x2 – 9)(x – 4)

(x2 + 9)(x – 4)

(x2 – 9)(x + 4)

Answer 1

Factor by grouping:

x^3 + 4x^2 – 9x – 36 = (x^3 + 4x^2) + (−9x − 36)
= x^2(x + 4) − 9(x + 4)
= (x + 4)(x^2 − 9).

So the correct choice is (x^2 − 9)(x + 4). (It further factors to (x + 4)(x − 3)(x + 3).)