How do you use the remainder theorem to find the remainder when $2x^3 – x^2 – 3x + 7$ is divided by x + 2?

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Answer 1 · 2015-08-22T02:38:30

The remainder is $-7$

The Remainder Theorem tell us that when polynomial $P(x)$ is divided by $x-c$ , the remainder is $P(c)$ .

When $P(x) = 2x^3 – x^2 – 3x + 7$ is divided by $x + 2$ ,

we are dividing by $x-(-2)$ , so the remainder will be:

$P(-2) = 2(-2)^3 – (-2)^2 – 3(-2) + 7$

$= -16-4+6+7 = -20 + 13 = -7$

How do you use the remainder theorem to find the remainder when 2x^3 – x^2 – 3x + 72x^3 – x^2 – 3x + 7 is divided by x + 2?