f(x) = (-x^2)(e^-x) + 2xe^-x
finding the zeros of this darn function, help please
That's the purpose of factoring, writing an expression as a product.
Fact: Zero multiplied by anything is zero because any amount of zeros is zero.
So, can we factor that ?
Yes, there is a common factor $\displaystyle x$ and another $\displaystyle e^{-x}$
$\displaystyle -x^2e^{-x}+2xe^{-x}=xe^{-x}(2-x)=(x)\left(e^{-x}\right)(2-x)$
Now you can see which values of x causes that to be zero.