(x +1) is a factor of the polynomial:
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