7.5 - Perfect Square Trinomials

 Introduction:

This is a set of guiding questions and materials for creating your own lesson plan on factoring perfect square trinomials.

 Common Core State Standards:

A.SSE.2

 Learning Objectives:

• To identify patterns in trinomials.
• To factor perfect square trinomials.

• What do you notice in these four products?
• What is (x + 1)(x + 2)?
• What is (x + 2)(x + 3)?
• What is (x + 3)(x + 4)?
• What is $x^2+9x+20?$
• Can you factor $x^2+10x+21?$
• What do you notice?
• Can we generalize?
• $\left(x+a\right)\left(x+b\right)=x^2+ax+bx+ab=x^2+\left(a+b\right)x+ab$
• $\left(x+a\right)\left(x+b\right)=x^2+\left(a+b\right)x+ab$
• What about these three?
• (x + 3)(x – 5)
• (x – 3)(x + 5)
• (x – 3)(x – 5)
• How do these relate to the previous ones?
• How do you factor $15x^2+11x+2?$
• Can you generalize the method used?
• $\left(ax+b\right)\left(cx+d\right)=acx^2+x\left(ad+bc\right)+bd$

7.5.1 Factoring Trinomials

Generalization of the factorization of some trinomials

7.5.1 Factoring More Trinomials-1.mp4 Download 7.5.1 Factoring More Trinomials-1.mp4Play media comment.

7.5.2 Bottoms-up Technique: Case 1

Demonstration of the bottoms-up technique

 7.5.2 Bottoms-up Case 1.mp4 Download 7.5.2 Bottoms-up Case 1.mp4Play media comment.

7.5.3 Bottoms-up Technique: Case 2

Demonstration of the bottoms-up technique with pulling out GCF

7.5.3 Bottoms-up Case 2.mp4 Download 7.5.3 Bottoms-up Case 2.mp4Play media comment.

• North Carolina Common Core Math 1 Item Bank, Nagy-Lup, pp.18-19

• If the area of a rectangle is given by $6x^2+17x+12$ and the width is $\left(2x+3\right)$, what is the length in terms of x?

• Khan Academy: Factoring Quadratics Links to an external site.