# How do you use the remainder theorem to determine the remainder when the polynomial #x^4+x^3-5x^2+2x-7# is divided by #x+2#?

##### 1 Answer

Dec 23, 2016

The remainder is the result of substituting

#### Explanation:

#f(x) = x^4+x^3-5x^2+2x-7#

The remainder when divided by

So the remainder when divided by

#f(-2) = 16-8-20-4-7 = -23#

Here is a long division of the coefficients, just to check:

So:

#x^4+x^3-5x^2+2x-7 = (x^3-x^2-3x+8)(x+2)-23#