Factorize

x³ – 3x² – 9x – 5

Let p(x) = x³ – 3x² – 9x – 5

By trial, we find that p(–1) = 0, so by Factor theorem,

(x + 1) is the factor of p(x)

When we divide p(x) by (x + 1), we get x² – 4x – 5.

Now, (x² – 4x – 5) is a quadratic and can be solved by splitting the middle terms.

We have x² – 4x – 5 = x² – 5x + x – 5

⇒ x (x – 5) + 1 (x – 5)

⇒ (x + 1)(x – 5)

So, x³ – 3x² – 9x – 5= (x + 1)(x + 1)(x – 5)