Imaginary/Real zeros of function

The problem says

State how many imaginary and real zeros the function has.

f(x) = x^{3} + 5x^{2} + x + 5

I take an online course, and the one and only video this give me this time is god awful. I have no idea how to figure this out. Please help me. And if you could please explain it, I'd like to actually learn how to do this, not just get an answer.

Thank you so much.

Re: Imaginary/Real zeros of function

$\displaystyle x^3 + 5x^2 + x + 5 = 0$

factor by grouping ...

$\displaystyle x^2(x+5) + (x+5) = 0$

$\displaystyle (x+5)(x^2 + 1) = 0$

one real zero ... $\displaystyle x = -5$

two imaginary zeros ... $\displaystyle \pm i$