Divide using long division. (x^3+6x^2−x−30)÷(x−2)
Before we begin dividing, let's first arrange the terms in descending order:
x^3 + 6x^2 - x - 30
Now, let's divide using long division:
________
x - 2 | x^3 + 6x^2 - x - 30
- (x^3 - 2x^2)
______________
8x^2 - x
- (8x^2 - 16x)
______________
15x - 30
- (15x - 30)
______________
0
Therefore, the quotient is x^2 + 8x + 15.