Taking Out a Common Factor — Cheat sheet

Key method

The distributive law works in reverse:

A polynomial factor can also be common. Keep its parentheses intact while treating it as one object.

Example

In $18x^3y-12x^2y^2$, the coefficient factor is $6$, and the shared variable part is $x^2y$. Thus

For $x(x+1)+4(x+1)$, the repeated object is $x+1$, giving $(x+1)(x+4)$.

Avoid this mistake

Do not take a variable outside if it is absent from one term. For example, $x^2+3$ has no common factor $x$ as a polynomial.