Toolkit 100

Factor Theorem

If P(x) is a polynomial and P(r)=0, then (x-r) is a factor of P(x).

P(r)=0(xr)P(x)P(r)=0\quad\Longrightarrow\quad (x-r)\mid P(x)

To factor a polynomial of degree at least 3, one useful approach is to find a root r first. Then (x-r) is a factor, allowing further factorization.