Summary of factoring techniques

Here are the steps for factoring polynomials in Beginning Algebra: These techniques will work for all polynomials up to degree 2 and for some polynomials of higher degree.

For definiteness, here are the conditions that must be met for a polynomial (with rational coefficients) to be completely factored:

The last of these is the one that can be hard to check and may require fancy techniques to fix.

A product of two non-constant polynomials is called a composite polynomial. (The last rule above requires us to factor these polynomials further.) A non-constant polynomial that is not composite is called a prime polynomial. (The constant polynomials are considered neither prime nor composite.) Compare that a product of two whole numbers greater than 1 is called a composite number, while a whole number greater than 1 that is not composite is called a prime number. (The whole numbers 0 and 1 are neither prime nor composite. In this analogy, the non-zero constant polynomials correspond to the whole number 1, while the constant polynomial 0 corresponds to the whole number 0.)

Go back to the course homepage.
This web page was written between 2010 and 2018 by Toby Bartels, last edited on 2018 August 28. Toby reserves no legal rights to it.

The permanent URI of this web page is