Chapter 10 5 Solving Quadratic Equations by Factoring

Chapter 10. 5 Solving Quadratic Equations by Factoring

FOIL method - Used for multiplying 2 binomials (x+7)(x+4) = x 2 + 11 x + 28 What do 11 and 28 have in common?

Factoring • Basically it is doing FOIL in reverse • Or, doing the distributive property in reverse

Remember the Factor Tree?

Remember the Factor Tree?

Factor x 2 + 21 x + 80 Factors of 80: Which ones add up to 21?

For factoring x 2 + bx + c = 0 (When there is not a number in front of x 2) 1. Enter x as the first term of each factor (x + ) = 0 2. List all pairs of factors of “c”. 3. Try various combinations of these factors to find two factors that add up to “b”. (x + __) = x 2 + bx + c These two numbers should add up to “b” 4. Check your work by using FOIL.

Homework • Section 10. 5 – Page 607, # 15 -26

• Section 10. 5 – Page 607, # 15 -26

• Section 10. 5 – Page 607, # 15 -26

Another type of Factoring • Un-doing the distributive property Example: 8 x 2 + 32 x What common factors are in both terms?

Another type of Factoring • Un-doing the distributive property Example: 9 x 2 - 27 x What common factors are in both terms?

Another type of Factoring • Un-doing the distributive property Example: 6 x 4 + 24 x 3 What common factors are in both terms?

Un-doing the distributive property

Un-doing the distributive property

Un-doing the distributive property