Question

How do you use the remainder theorem to see if the `p-2` is a factor of `p^4-8p^3+10p^2+2p+4`?

Answer 1

The remainder = 0, which means that `(p-2)` is a factor of the expression.

Explanation:

Let `f(p) = p^4-8p^3+10p^2+2p+4`

If `p-2 = 0 " "rarr p = 2`

Find `f(2)` which will give the remainder.

`f(2) = 2^4-8(2)^3+10(2)^2+2(2)+4`

`f(2) = 16-64+40+4+4 =0`

The remainder = 0, which means that `(p-2)` is a factor of the expression.