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

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Answer 1 · 2017-02-21T09:00:03

$8$

The remainder theorem states that a polynomial $P(x)$ is divided by $(x-a)$ the remainder is $P(a)$

so for $P(x)=2x^3+3x^2-5x+2$

the remainder on dividing by $(x+2) " is " P(-2)$

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

$P(-2)=2xx-8+3xx4+10+2$

$P(-2)=-16+12+10+2=8$

How do you use the remainder theorem to determine the remainder when the polynomial 2x^3+3x^2-5x+22x^3+3x^2-5x+2 is divided by x+2x+2?