Hello!
Can someone please help me with this problem?
8x^2e^x + x^3e^x = 0
I'm still having problems understanding the steps...
Thanks!
The key to these problems is that $\displaystyle e^x$ is a common term to each, so it can be factored out, along with other powers of x.
$\displaystyle 8x^2e^x + x^3e^x =x^2e^x (8+ x)= 0$
When you factor out the $\displaystyle e^x$, remember, it can never be zero.
Then the only way for $\displaystyle x^2e^x (8+ x)= 0$ to be true is for
$\displaystyle e^x=0$, which can't happen, so you can just ignore this factor at this point, and
you have either $\displaystyle x^2= 0$ or $\displaystyle (8+ x)= 0$