What are the simplest factors of this polynomial? x3 + 4x2 - 9x - 36

1. Factor out common terms in the first two terms, then in the last two terms:

x^2 (x + 4) - 9 (x + 4)

2. Factor out the common term x + 4

(x + 4) (x^2 - 9)

3. Rewrite x^2 - 9 in the form a^2 - b^2, where a = x and b = 3

(x + 4) (x^2 - 3^2)

4. Use Difference of Squares: a^2 - b^2 = (a + b) (a - b)

(x + 4) (x + 3) (x - 3)