1. Solve for X

Hello!

8x^2e^x + x^3e^x = 0

I'm still having problems understanding the steps...

Thanks!

2. The key to these problems is that $e^x$ is a common term to each, so it can be factored out, along with other powers of x.

$8x^2e^x + x^3e^x =x^2e^x (8+ x)= 0$

When you factor out the $e^x$, remember, it can never be zero.

Then the only way for $x^2e^x (8+ x)= 0$ to be true is for

$e^x=0$, which can't happen, so you can just ignore this factor at this point, and

you have either $x^2= 0$ or $(8+ x)= 0$

3. great thanks! so to my undestanding e^x can always be eliminated as long as it has a common factor?

4. flipboi:"great thanks! so to my undestanding e^x can always be eliminated as long as it has a common factor?"

if there is a common factor in every TERM, then do the factoring as may..