Find all values of a for which x2-ax2+(a+1)x-2 is divisible by x-a.

Question

I know you are supposed to do synthetic division, but I have no clue what to do after that. I have tried searching up what to do but nothing comes up

Answer 1

It doesn't matter how you do the division, you need to get the remainder, which is

-2 + a + 2a² - a³

and set the remainder = 0.

The remainder factors into (a - 1)(a - 1)(a + 2) which gives you the values of a.