Lesson Plan 4.4: Factoring Trinomials

Objectives:

Factoring trinomials no matter what the coefficient of the second degree term is.

It is suggested to simply teach the ``a-c method" of factoring, since it works for both a coefficient on the leading term of 1 and not 1 (refer to the Guide to Factoring).
List out the steps of the a-c method on the side of one board, and carry out various examples (at least 3), being explicit in how you find the correct pair of numbers that multiply to ac. For example:
- 15x^2-28x+5 factors as (5x-1)(3x-5). Our product ac is: 15*5=5*5*3=25*3=-25*-3, and -25+-3=-28.
- 4a^2-14a-30 factors as 2(a-5)(2a+3)
- 4a^2-14a-30=2(2a^2-7a-15) and our product, ac, is: 2*(-15)=-2*5*3=-10*3 and -10+3=-7.
- 6x^2+3x-9 factors as 3(x-1)(2x+3): 3(2x^2+x-3), choose 3 and -2.
Make sure to include at least one example where the ac method is preceded by factoring out a GCF.
Also make sure to encourage students to check their final answer by foiling.
While we do not teach other methods, students may use other (valid) methods for factoring. To receive credit on quizzes/exams, they must show their work. If they claim to just be able to do it in their heads (for example: x^2+3x-10)=(x-2)(x+5)) then they may show their work by foiling out their factored form, and comparing it to the original problem.

Encourage students to be thorough in the work and go one step at a time so that they may pay attention to plus and minus signs and the like. Also encourage them to write down the various pairs they could choose to multiply to $ac$ as they are first learning.

The OER on this sections was significantly changed on 11/14/19 to only discuss the $ac$-method instead of including the "trial and error" method. Some students may have read the OER before it was updated and may have questions about the method that was removed.