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???

Guest Jun 15, 2018

#1**+1 **

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**

Guest Jun 15, 2018