Overview
On this page, we review how to factor trinomials, i.e. polynomials with exactly three terms (most of the time, we will consider quadratic trinomials of the form \(ax^2+bx+c\), possibly multiplied by a monomial), using the “ac-method”.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Use the “ac-method” to factor a quadratic trinomial.
- Factor out the GCF and then use the “ac-method” to completely factor a trinomial.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Factor trinomials with leading coefficient \(a=1\) efficiently, by using the special case of the ac-method, the so-called “Sum-Product Rule” or “Vieta’s Formula”.
To prepare for class
-
Watch the following videos (by Tyler Wallace) which explain the so-called “ac-method” to factor a trinomial with leading coefficient \(a\neq 1\):
-
Watch the following videos (by Tyler Wallace) which explain how to use the “ac-method” (when \(a\neq 1\)) after first factoring out the GCF:
After class
-
Watch the following videos (by Tyler Wallace) which explain the special case of trinomials with leading coefficient \(a=1\): In this case, the “ac-method” simplifies to a method which is commonly called “Sum-Product Rule” or “Vieta’s Formula”:
