Question

If a polynomial $f\left(x\right)$ is divided by $x^2-16$ then remainder is $5x+3$, what will be the remainder when the same polynomial is divided by $(x+4)$?

Answer 1

Let the quotient be $q\left(x\right)$

$f\left(x\right)=(x^2-16)+(5x+3)$

$\frac{f\left(x\right)}{(x+4)}=\frac{(x+4)(x-4)}{x+4}q\left(x\right)+\frac{5x+3}{x+4}$

Remainder=Remainder when $5x+3$ is divided by $x+4$

$=5(-4)+3=-17$