What is the sum of the \(x\) values that satisfy the equation \(5=\frac{x^3-2x^2-8x}{x+2}\)?
I cross multiplied and got: 5x + 10 = x^3 - 2x^2 - 8x.
What should I do next???
Solve for x:
5 x + 10 = x^3 - 2 x^2 - 8 x
Subtract x^3 - 2 x^2 - 8 x from both sides:
-x^3 + 2 x^2 + 13 x + 10 = 0
The left hand side factors into a product with four terms:
-(x - 5) (x + 1) (x + 2) = 0
Multiply both sides by -1:
(x - 5) (x + 1) (x + 2) = 0
Split into three equations:
x - 5 = 0 or x + 1 = 0 or x + 2 = 0
Add 5 to both sides:
x = 5 or x + 1 = 0 or x + 2 = 0
Subtract 1 from both sides:
x = 5 or x = -1 or x + 2 = 0
Subtract 2 from both sides:
x = 5 or x = -1 or x = -2
