Find All values of a for which x^2-ax^2+(a+1)x-2 is divisible by x-a

Question

I really need help with this.

Answer 1

(x^2-ax^2+(a+1)x-2)/(x-a)=(1-a)x+(1+2a-a^2)-(a^3-2a^2-a+2).

Therfore, to be divisible by x-a 

a^3-2a^2-a+2=0

from which follws that a can be -1, 1 and 2.

 

a^3-2a^2-a+2=0

(a-2)(a^2-1)=0