Question

The graph of f(x) = x3 + x2 – 9x – 9 is shown.


Based on the graph, what are the solutions of x3 + x2 – 9x – 9 = 0?

x = –1, 3
x = –3, –1
x = –3, –1, 3
x = –9, –3, –1, 3

Answer 1

Factor by grouping: x^3 + x^2 − 9x − 9 = x^2(x+1) − 9(x+1) = (x+1)(x^2 − 9) = (x+1)(x−3)(x+3).

So the solutions are x = −3, −1, 3.