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

Question

3600 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-11T04:46:08

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

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

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

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

$=4$

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)=a3+5a2+10a+12f(a)=a^3+5a^2+10a+12 at a=-2?