Question

Consider the polynomial division (x^3+5x^2+4x+18)/(x+5). Give the quotient with the remainder expressed as a fraction.

-27/(x+5) is not the answer

Answer 1

To divide the polynomial (x^3+5x^2+4x+18) by (x+5), we can use long division.

x^2 - 4x + 16
___________________________________
x + 5 | x^3 + 5x^2 + 4x + 18
- (x^3 + 5x^2)
_____________
- 4x + 18
- (- 4x + 20)
_____________
- 2

The quotient is x^2 - 4x + 16, and the remainder is -2.

Therefore, the polynomial division (x^3+5x^2+4x+18)/(x+5) can be expressed as:

x^2 - 4x + 16 - 2/(x+5)