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 $x+2$ ?

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Answer 1 · 2016-12-23T16:17:28

The remainder is the result of substituting $x=-2$ , namely $-23$

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

The remainder when divided by $(x-a)$ is $f(a)$ .

So the remainder when divided by $(x+2)$ is:

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

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

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So:

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

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