Question

Factor w^3 + 3w^2 – w – 3.

w^2(w + 3) – (w + 3)

w(w^2 + 3w – 1) – 3

(w + 3)(w + 1)(w – 1)

Answer 1

Factor by grouping:

w^3 + 3w^2 − w − 3 = (w^3 + 3w^2) + (−w − 3)
= w^2(w + 3) − 1(w + 3)
= (w + 3)(w^2 − 1)
= (w + 3)(w + 1)(w − 1).

Comments on your lines:
- w^2(w + 3) − (w + 3) is the correct grouping step.
- w(w^2 + 3w − 1) − 3 is algebraically equal to the original but not a useful factorization.
- (w + 3)(w + 1)(w − 1) is the correct full factorization.