Question

Find the remainder when the polynomial $f\left(x\right)=2x^4-6x^3+2x^2-x+2$ is divided by x + 2

Answer 1

We have, x + 2 = x - (-2). So, by remainder theorem, when f(x) is divided by (x-(-2)) the remainder is equal to f(-2).
Now, $f\left(x\right)=2x^4-6x^3+2x^2-x+2$
$\Rightarrow$ $f(-2)=2(-2{)}^4-6(-2{)}^3+2(-2{)}^2-(-2)+2$
$\Rightarrow$ $f(-2)=2\times 16-6\times -8+2\times 4+2+2$
$\Rightarrow$ $f(-2)=32+48+8+2+2=92$
Hence, required remainder = 92.