x^3 + 2x^2 - 9x - 18 = (x^2 - a^2)(x + b) where a,b are integers. Work out the three linear factors of x^3 + 2x^2 - 9x - 18. (Note: x^3 indicates x cubed and x^2 indicates x squared).

There are a few different ways to approach this problem. The most obvious is to attempt to factorise x³ + 2x² - 9x - 18. However it is very difficult to approach the problem like this. fortunately the question has given us that the cubic expression factorises to(x²-a²)(x+b). If we expand this back out we get x³ + bx² - a²x - a²b. We can then compare this cubic to our original and see that a² = 9 and b = 2.

So we now have x³+2x²-9x-18 = (x²-9)(x+2). We know that we can factorise x²-9 to (x+3)(x-3) so our linear factorisation of the original cubic is (x+3)(x-3)(x+2).