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}`