7.5 Factoring Trinomials
This is a set of guiding questions and materials for creating your own lesson plan on factoring
trinomials.
Common Core State Standards: A.SSE.2
Learning Objectives
 To identify patterns in trinomials.
 To factor perfect square trinomials.
 To factor trinomials.
Guiding Questions
 What do you notice in these products?
o What is (x + 1)(x + 2)?
o What is (x + 2)(x + 3)?
o What is (x + 3)(x + 4)?
 What is x2 + 9x + 20?
 Can you factor x2 + 10x + 21?
 What do you notice?
 Can we generalize?
o (x + a)(x + b) = x2 + ax + bx + ab = x2 + (a+b)x + ab
o (x + a)(x + b) = x2 + (a+b)x + ab
 What about these three?
o (x + 3)(x – 5)
o (x – 3)(x + 5)
o (x – 3)(x – 5)
 How do these relate to the previous ones?
 How do you factor 15x2 +11x + 2?
 Can you generalize the method used?
o (ax+b)(cx+d) = acx2 + x(ad+bc) + bd
Notes for Teachers
 As teachers, we strive to elicit from students answers to relevant questions as we let
them explore mathematical objects and ideas.
Video of the Day
 7.5.1 A Factoring Generalization for Trinomials
o Description: Generalization of the factorization of some trinomials
o Tags: factoring trinomials, Hector Rosario, polynomials, A.SSE.2
 7.5.2 A Factoring Generalization for Trinomials
o Description: Demonstration of the bottoms-up technique
o Tags: Bottoms-up, factorization, trinomials, Hector Rosario
 7.5.2 A Factoring Generalization for Trinomials
o Description: Demonstration of the bottoms-up technique with pulling out GCF
o Tags: Bottoms-up, factorization, trinomials, Hector Rosario
Exercises and Problems
 North Carolina Common Core Math 1 Item Bank, Nagy-Lup, pp. 18-19

If the area of a rectangle is given by 6x2 + 17x + 12 and the width is (2x + 3), what is
the length in terms of x?
Online Resources
 Khan Academy: Factoring quadratics