Chapter 5.2Solving Quadratic Equations by

Factoring

A Quadratic Equation is in this form:

ax2 + bx + c = 0

Examples:x2 + 4x + 5 = 02x2 + 7x - 12 = 04x2 – 8x - 18 = 0

Binomial – an algebraic expression that contains two terms

Examples of binomialsx + 7x – 37x – 139x + 21

Multiplying Binomials

(x + 3) (x + 2)

We can use the FOIL methodF = first termsO = outer termsI = inner termsL = last terms

(x + 3) (x + 2)

First terms = x times x which is x2

Outer terms = x times 2 2x

Inner terms = 3 times x 3x

Last terms = 3 times 2 6

X2 + 2x + 3x + 6 = x2 + 5x + 6

(x – 9)(x + 5)

(x – 9)(x + 5) Use FOIL

= x2 + 5x - 9x – 45

Simplify= x2 – 4x - 45

(3x + 3)(2x + 5)

(3x + 3)(2x + 5) Use FOIL

= 6x2 + 15x + 6x + 15

Simplify= 6x2 + 21x + 15

X2 + 7x + 12

This expression is called a Trinomial.

We can use the FOIL method to multiply two binomials to get this trinomial X2 + 7x + 12.

(x+4) (x+3) = X2 + 3x + 4x + 12 = X2 + 7x + 12

X2 + 7x + 12 = (x+4) (x+3)

X2 is the product of x and x

X2 + 7x + 12 = (x+4) (x+3)

12 is the product of 4 and 3

X2 + 7x + 12 = (x+4) (x+3)

7x is the sum of the outside and inside products, 3x and 4x

Factoring A Trinomial

….Basically you are doing FOIL in reverse

Factor x2 + 6x + 8

Set up x as the first terms of each factor:(x + ? ) (x + ? )

List all pairs that are factors of the last number 81 and 8, 2 and 4

Which of these pairs add up to 6?4 and 2

The solution is (x + 4) (x + 2)

For factoring x2 + bx + c = 0(When there is not a number in front of x2)

1. Enter x as the first term of each factor(x + ) (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 + __) = x2 + bx + c

These two numbers should add up to “b”

4. Check your work by using FOIL.

Factor x2 - 3x - 18

Factors of -18: -3*6; 3*-6; 2*-9, -2*9;-1*18,1*-18

Which ones add up to -3? 3*-6

Solution: (x+3) (x-6)

Classwork / Homework• Page 260, #23 - 34