Question

Using the remainder theorem, find the remainder when $f\left(x\right)=x^3+4x^2-3x+10$ is divided by $g\left(x\right)=(x+4)$.

Answer 1

Given:
$f\left(x\right)=x^3+4x^2-3x+10$
$g\left(x\right)=x+4$
$g\left(x\right)=x=-4$
We have to find the remainder when f(x)is divided by g(x).
By applying remainder theorem, when f(x)is divided by g(x) we get,

Step 1:
$f(-4)=-(4{)}^3+4(-4{)}^2-3(-4)+10.$

Step 2:
$f(-4)=-64+64+12+10=22.$
Hence, when f(x) = $x^3+4x^2-3x+10$ is divided by $g\left(x\right)=x+4$ we get the remainder as 22