Question

How do you factor `x^3 -3x-2=0`?

Answer 1

`x^3-3x-2=color(green)((x+1)(x+1)(x-2))`

Explanation:

Given:
`color(white)("XXX")color(red)(1)x^3-color(blue)(3)x-color(red)(2)`
Note that `color(red)(-1-2)=color(blue)(-3)`
which implies `x=-1` is a solution to the given equation
and therefore
`color(white)("XXX")(x+1)` is a factor of the expression:

`(x^3-3x-2) div (x+1) = (x^2-x-2)`
`color(white)("XXX")`use polynomial long division or some other method to get this

`x^2-2-2` can be factored normally as `(x+1)(x-2)`