Answer :

Let p(x) = x3 – 2x2 – 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 x2 – x – 2.


Now, (x2 – x – 2) is a quadratic and can be solved by splitting the middle terms.


We have x2 – x – 2 = x2 – 2x + x – 2


x (x – 2) + 1 (x – 2)


(x + 1)(x – 2)


So, x3 – 2x2 – x + 2 = (x – 1)(x + 1)(x – 2)


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