Question

Divide using long division. (x^3+6x^2−x−30)÷(x−2)

Answer 1

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.