Question

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

Answer 1

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(4)=-19` which you can test by direct substitution