Factorising polynomials

Factor theorem

If a $(ax-b)$ is a factor of a polynomial $P(x)$, then $P(\frac{b}{a})=0$.

Remainder theorem

Instead of dividing a polynomial entirely, we can use the following equation to calculate the remainder of division by a linear polynomial:

$P(x)=Q(x)(ax-b)+\frac{b}{a}$

Then the remainder is equal to $\frac{b}{a}$.