Answer :

Let p(x) = x^{3} – 2x^{2} – x + 2

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 x^{2} – x – 2.

Now, (x^{2} – x – 2) is a quadratic and can be solved by splitting the middle terms.

We have x^{2} – x – 2 = x^{2} – 2x + x – 2

⇒ x (x – 2) + 1 (x – 2)

⇒ (x + 1)(x – 2)

So, x^{3} – 2x^{2} – x + 2 = (x – 1)(x + 1)(x – 2)

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