Question

How do you use the factor theorem to determine whether b+1 is a factor of `b^6 – b^5 – b + 1`?

Answer 1

`b+1` is NOT the factor of `b^6-b^5-b+1`

Explanation:

To check if `(x-a)` is a factor of `P(x)` you have to check if `P(a)=0`

In this case `a=-1` so you have to find `P(-1)`

`P(-1)=(-1)^6-(-1)^5-(-1)+1=1+1+1+1=4`

`P(-1)!=0`, so `(x+1)` is NOT the factor of `P(x)`