Question
Consider the polynomial division (x^3+5x^2+4x+18)/(x+5). Give the quotient with the remainder expressed as a fraction.
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You were wrong last time
Answers
Answered by
GPT 3.5
I apologize for any confusion caused. To perform polynomial division, let's divide (x^3+5x^2+4x+18) by (x+5).
- x^2 + 6x - 10
_______________________
x + 5 │ x^3 + 5x^2 + 4x + 18
- (x^3 + 5x^2)
________________
-x^2 + 4x
+ ( -x^2 - 5x)
________________
9x + 18
- (9x + 45)
_______________
-27
The quotient is -x^2 + 6x - 10 and the remainder is -27. Therefore, the polynomial division (x^3+5x^2+4x+18)/(x+5) gives the quotient as -x^2 + 6x - 10, with the remainder expressed as -27/ (x+5).
- x^2 + 6x - 10
_______________________
x + 5 │ x^3 + 5x^2 + 4x + 18
- (x^3 + 5x^2)
________________
-x^2 + 4x
+ ( -x^2 - 5x)
________________
9x + 18
- (9x + 45)
_______________
-27
The quotient is -x^2 + 6x - 10 and the remainder is -27. Therefore, the polynomial division (x^3+5x^2+4x+18)/(x+5) gives the quotient as -x^2 + 6x - 10, with the remainder expressed as -27/ (x+5).