Find the complex zeros of the following polynomial function. Write f in the factored form.

Question

F(x)=2x^4-5x^3-20x^2+115x-52

Answer 1

Look for the low-hanging fruit first. No easy roots, like 1 or 2, but we do find

F(x) = (x+4)(2x^3-13x^2+32x-13)
=(x+4)(2x-1)(x^2-6x+13)

Now use the quadratic formula for the complex roots.

This one was a little messy, since the roots took a little trial and error. Synthetic division comes in handy here.