Explore the Lesson

A. Greatest Common Factors

Polynomials, like numbers, can be expressed as a product of their factors. To express a polynomial as a product of its factors, it is necessary to identify factor(s) common to all of the terms in the polynomial. One way to do this is to focus on the greatest common factor (GCF) of the polynomial's terms. Because the GCF is common to all terms, it can be moved outside a set of brackets using the distributive property in reverse. This process is demonstrated using the expression 15 − 25 + 40.

Step Example
Determine the GCF of the three terms.
The GCF of 15, −25, and 40 is 5.
Write each term as the product of the GCF and another factor.
Use the distributive property in reverse to write the original expression as a product of two factors.
Use the distributive property to verify that the original expression was factored properly.

 

Factors
two or more numbers or expressions that are multiplied to give a product

Factoring a Polynomial
the decomposition of a polynomial into a product of its factors, which when multiplied together give the original polynomial

Greatest Common Factor (GCF) of Polynomials
the greatest common factor of a polynomial is the polynomial of highest degree and largest coefficient that is a factor of all of the terms in the original polynomial


In this lesson, you will look at how each of the steps shown in the table above can be performed with polynomials.