How do you use the remainder theorem to evaluate $f(a)=a^3+5a^2+10a+12$ at a=-2?

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Answer 1 · 2017-10-11T04:46:08

the remainder of the division $(a^3+5a^2+10a+12):(a+2)$ is 4

We simply will substitute $a=-2$ in $f(a)$ :

$f(-2)=(-2)^3+5(-2)^2+10(-2)+12$

$=-8cancel+20cancel(-20)+12$

$=4$

that means the remainder of the division:

$(a^3+5a^2+10a+12):(a+2)$

is 4

How do you use the remainder theorem to evaluate f(a)=a^3+5a^2+10a+12f(a)=a^3+5a^2+10a+12 at a=-2?