To what extent do I need my mathematical knowledge to become a professional game programmer? I am fine with everything but factoring. I''ll think I know how, then totally mess up. So is factoring neccessary?

If by factoring you mean stuff like

ab + ac = a(b +c)

then this is useful. Good skills with algebra are useful as they let you rearrange and simplify problems into the best form for using in a computer program.

Basic algebra skills are also important as they are used in more advanced topics such as calculus, trigonometry, etc. which form the basis of most simulations in games.