Hi all! having some trouble with this question and have an exam in 3 days so hoping to get some help! leaving it late, I know.

Anyway, so $\displaystyle f(x)= x^4 - 3x^3+6x^2+2x-60$ is the polynomial and 1+3i is the complex zero.

So I used synthetic division to obtain this 1 4+3i 1+15i - 42+18i remainder -36-108i

Then I used 1-3i, the conjugate which should also be a zero, yes? to obtain: 1 5 6 -36 and a remainder of -72 for my co-efficients. Which if the sign had been reversed I would have had an nice neat 0 remainder and I could have gone on from there but ive been over my working twice and cant find any mistakes I made- I am hoping that I have, as that means I don't have to learn how to deal with these remainders.

Hoping someone can help me out here, thanks so much!

Rhys