In the previous lesson, we've seen how to factor trinomials with the coefficient of 1 for the squared term. Now, we are going to factor trinomials when the coefficient of the squared term is not 1. This is a little bit more complicated. If the coefficient on the squared term is not one, then reverse FOIL may still work. There will be many more possibilities to check for the terms in your binomials. In this lesson you are going to learn how to use the AC method, which deals with the A and C coefficients. Be very careful with your signs when using this method.
If the coefficient on the squared term is not one, then reverse FOIL may still work. There will be many more possibilities to check for the terms in your binomials.
To use the AC method
Start by making sure all terms have a greatest common factor of one
Multiply the A and C coefficients together
Find two numbers that multiply to give you AC but add to give you B
Split up the middle term of the trinomial using the numbers found in step 3
Factor the polynomial by using factor by grouping
Be very careful with your signs when using the AC method.
It is often helpful to write down all pairs of numbers that multiply to AC.
When factoring is complete, check your work by using FOIL on the binomials. They should multiply to give you the original trinomial.
Factoring Trinomials Using the AC Method
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.