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)
x + 4 is prime

x2 – 9 can be factored using the
formula.

Answer 1

Group terms: x^3 + 4x^2 − 9x − 36
= x^2(x + 4) − 9(x + 4)
= (x + 4)(x^2 − 9).

Then factor x^2 − 9 as a difference of squares: x^2 − 9 = (x − 3)(x + 3).

So the full factorization is (x + 4)(x − 3)(x + 3). The matching choice from your list is (x^2 − 9)(x + 4).