Q. 27

# (x +1) is a facto

We have, (x + 1) = 0

x = - 1

Firstly, putting (x = - 1) in x3 – 2x2 + x + 2 we get:

= (- 1)3 – 2 (-1)2 + (-1) + 2

= - 1 – 2 – 1 + 2

= - 2

(x + 1) is not a factor of x3 – 2x2 + x + 2

Secondly, putting (x = - 1) in x3 + 2x2 + x - 2 we get:

= (-1)3 + 2 (-1)2 + (-1) – 2

= - 1 + 2 – 1 – 2

= - 2

(x + 1) is not a factor of x3 + 2x2 + x – 2

Thirdly, putting (x = - 1) in x3 + 2x2 – x – 2 we get:

= (-1)3 + 2 (-1)2 – (-1) – 2

= - 1 + 2 + 1 – 2

= 0

Hence, (x + 1) is a factor of x3 + 2x2 + x – 2

Thus, option C is correct

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