Question

The remainder after diving x^4+3x^3-8x^2+5x-9 by x+5 is ____.

Answer 1

Use the polynomial remainder theorem. It says that a polynomial $f(x)$ has remainder $f(c)$ upon division by $x-c$.

Here we have

$f(x)=x^4+3x^3-8x^2+5x-9$

and $c=-5$, so the remainder is

$f(-5)=(-5)^4+3(-5)^3-8(-5)^2+5(-5)-9=\boxed{16}$