Factoring Polynomials with Exponents: Help Needed

[ggcheck]

Homework Statement

I need to find the critical points of
f(x) = (x^3 - 2x)e^x

I found the derivative, and set it equal to zero

ended up with e^x (x^3 +3x^2 -2x -2) = 0

I am having trouble factoring the second factor, any suggestions?

 

[rock.freak667]

let f(x)=x^3 +3x^2 -2x -2
try f(1) and see what happens...

 

[ggcheck]

yeah I found f(1) just by looking at it, but how can I solve it without guessing?
+ there might be more solutions?

 

[rock.freak667]

Well if f(1)=0 then it means that (x-1) is a factor of f(x) just divide the polynomial by that linear factor and you'll get the other quadratic factor and then you can solve...Remember the remainder and factor theorem?

 

[ggcheck]

lol, wow I guess that was a while ago

thanks