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

Answer 1

To find the quotient with the remainder, we can use polynomial long division.

x^2 - 4x + 14
___________________
x + 5 | x^3 + 5x^2 + 4x + 18
- (x^3 + 5x^2)
_______________
-x^2 + 4x
+ (-x^2 - 5x)
_______________
9x + 18
- (9x + 45)
_______________
-27

Therefore, the quotient is x^2 - 4x + 14 and the remainder expressed as a fraction is -27/(x + 5).