Question

The remainder after dividing x4 + 3x3 − 8x2 + 5x − 9 by x + 5 is

Answer 1

(x^4+3x^3-8x^2+5x-9)/(x+5)

x^3 remainder -2x^3-8x^2+5x-9
-2x^2 remainder 2x^2+5x-9
2x remainder -5x-9
-5 remainder 16

(x+5)(x^3-2x^2+2x-5)+16/(x+5)

so the remainder after division is:

16/(x+5)

Answer 2

16 is the remainder of the division.

Explanation:

The given equation is
`x^(4) + 3x^(3) -8x^(2) + 5x - 9` and we have to divide this expression by x = (-5)

We can find the remainder by synthetic division

-5 | 1 3 -8 5 (-9)

-5 10 -10 25

---------------------------------------

1 -2 2 -5 16

We can rewrite the expression as
`(x+5)(x^(3)-2x^(2)+2x-5)+16`

Therefore, remainder of the division is 16.