# How do you use the Remainder Theorem To Find P(x)=x^(4)-x^(3)-19x^(2)+31x-31 ; k=4?

Mar 18, 2016

Divide by x-4

#### Explanation:

Remainder theorem that says if you divide by x-4, the remainder will be equal to P(4).

We can set up synthetic division:

4 || 1 -1 -19 31 -31
4 12 -28 12
---------------------------------
1 3 -7 3 -19

So $P \left(4\right) = - 19$ which you can test by direct substitution