Chapter 5.2 Solving Quadratic Equations by Factoring

A Quadratic Equation is in this form: ax 2 + bx + c = 0 Examples: x 2 + 4x + 5 = 0 2x 2 + 7x - 12 = 0 4x 2 – 8x - 18 = 0

Binomial – an algebraic expression that contains two terms Examples of binomials x + 7 x – 3 7x – 13 9x + 21

Multiplying Binomials (x + 3) (x + 2) We can use the FOIL method F = first terms O = outer terms I = inner terms L = last terms

(x + 3) (x + 2) First terms = x times x which is x 2 Outer terms = x times 2 2x Inner terms = 3 times x3x Last terms = 3 times 26 X 2 + 2x + 3x + 6 = x 2 + 5x + 6

(x – 9)(x + 5) (x – 9)(x + 5)Use FOIL = x 2 + 5x - 9x – 45 Simplify = x 2 – 4x - 45

(3x + 3)(2x + 5) (3x + 3)(2x + 5)Use FOIL = 6x x + 6x + 15 Simplify = 6x x + 15

X 2 + 7x + 12 This expression is called a Trinomial. We can use the FOIL method to multiply two binomials to get this trinomial X 2 + 7x (x+4) (x+3) = X 2 + 3x + 4x + 12 = X 2 + 7x + 12

X 2 + 7x + 12 = (x+4) (x+3) X 2 is the product of x and x

X 2 + 7x + 12 = (x+4) (x+3) 12 is the product of 4 and 3

X 2 + 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 x 2 + 6x + 8 Set up x as the first terms of each factor: (x + ? ) List all pairs that are factors of the last number 8 1 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 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 + ) (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 + __) = x 2 + bx + c These two numbers should add up to “b” 4. Check your work by using FOIL.

Factor x 2 - 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, #