# Was the “polynomial remainder theorem” known before polynomial long division was discovered?

Nowadays we can easily prove the following fact using polynomial long division:

If $a$ is a root of the polynomial $f$, then there exists a polynomial $g$ such that $f(x) = (x - a)g(x)$.

I can't imagine how to prove this without polynomial long division. I have two questions:

1. Who invented polynomial long division, and when?
2. Was the above theorem known before the discovery of polynomial long division? If so, how was it proven?
• Actually the first time I learned about this factorisation it was proved without the polynomial long division. You basically say that $f(x) = f(x) - f(a)$ and try to factorize that explicitly. – Maxime Lucas Apr 3 '15 at 15:55