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

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Answer 1 · 2017-09-29T18:13:01

$16$

the remainder theorem states that if

$P(x) " is divided by "(x-a)$

the remainder is $" "P(a)$

so we have

$P(x)=x^3+3x^2-5x+2" is divided by "x+2$

so the remainder will be $P(-2)$

$P(-2)=(-2)^3+3(-2)^2-5(-2)+2$

$P(-2)=-8+12+10+2$

$P(-2)=16$

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