Show that $\displaystyle x=-5$ is the only real root of cubic equation:

$\displaystyle x^3+3x^2-2x+40=0$

Can I do it this way?

(1) Fill for x=-5 and show that it equals zero.

(2) Divide factor (x+5) into the given cubic.This will give me a quadratic.

(3) Then show that $\displaystyle b^2-4ac<0$ which means no other real roots

Would this be a correct approach?