**Factoring a polynomial** is to find polynomials whose product is equal to the polynomial.

**A prime polynomial** is a polynomial that can not be factored as the product of two polynomials with lower degrees.

__Remark__ A prime polynomial in one variable has degree one or two.

**A completely factored polynomial** is a polynomial that is factored as a product of prime polynomials.

**Commonly used tricks in factoring polynomials**

Factoring out common factor:

Ex.

Grouping appropriate terms:

Ex.

Factor trinomials:
where and

Ex.

Using the formulas:

Ex.

Ex.

Ex.

Ex.

Ex.

Department of Mathematics