1. Day 147 – Factoring Trinomials

2. Example 1
Factor each polynomial. a. 4 𝑥 𝑥 2 −8𝑥 b. 36 𝑎 2 𝑏 4 −18 𝑎 3 𝑏 3

3. Answer
Factor each polynomial. a. 4 𝑥 𝑥 2 −8𝑥 =2∙2∙𝑥∙𝑥∙𝑥+2∙2∙2∙2∙𝑥∙𝑥−2∙2∙2∙𝑥 =4𝑥 𝑥 2 +4𝑥 4𝑥 −4𝑥 2 The GCF is 𝟒𝒙 =4𝑥( 𝑥 2 +4𝑥−2) Distributive property

4. Example 1
Factor each polynomial. b. 36 𝑎 2 𝑏 4 −18 𝑎 3 𝑏 3 =3∙3∙2∙2∙𝑎∙𝑎∙𝑏∙𝑏∙−3∙3∙2∙𝑎∙𝑎∙𝑎∙𝑏∙𝑏∙𝑏 =18 𝑎 2 𝑏 2 2 −18 𝑎 2 𝑏 2 (𝑎𝑏) The GCF is 18 𝑏 2 =18 𝑎 2 𝑏 2 (2−𝑎𝑏) Distributive property. To check that you factored correctly, multiply the factors. By removing the greatest common factor of a polynomial, you can present some geometric formulas in compact form.

5. Difference of Two Squares
When two binomials have first terms that are equal and last terms that are opposites they are called conjugates. The product of conjugates is called the difference of two squares.
𝒂 𝟐 − 𝒃 𝟐 =(𝒂+𝒃)(𝒂−𝒃)