If $a\neq 2$ and $a^3+a^2-a-10 = 0$, then evaluate $a+\frac{5}{a}$

Question

If $a\neq 2$ and $a^{3}+a^{2}-a-10 = 0$, then what is the value of $a+\dfrac{5}{a}$?

I have plugged equation on WolframAlpha and get the complex values of $a$ but you supposed to do this problem using factoring and very elementary algebra. I tried divide both sides of equation to get $a+\frac{5}{a}$, but the coefficients are given in a way that is hard to factor.

Answer 1

Just factor the given equation to get $(a-2)(a^2+3a+5)=0$. Since $a\neq2$, we must have $a^2+3a+5=0$. Now divide both sides by $a$ to get $$a+5/a=-3$$