1. 5.3 Factoring Quadratic Function 12/7/2012

2. are the numbers you multiply together to get another number: 3 and 4 are factors of 12, because 3x4=12. 2 and 5 are factors of 10, because 2x5=10 Vocabulary Factors: Examples:

3. Multiplying Binomials: FOIL First, Outside, Inside, Last Ex. (x + 3)(x + 5) ( x + 3)( x + 5) (x + 3)(x + 5) = x 2 + 5x + 3x +15 = x 2 + 8x + 15 I O L First: x x = x 2 Outside: x 5 = 5x Inside: 3x = 3x Last: 35 = 15 F To multiply 2 Binomials (expression with 2 terms) use FOIL. In this section, we’re going in reverse where the problem is Factoring x 2 + 8x + 15 and your answer is (x + 3) (x + 5)

4. The Big “X” method c b Think of 2 numbers that Multiply to c and Add to b #1#1 #2#2 add multiply Answer: (x ± # 1 ) (x ± # 2 ) Factor: x 2 + bx + c

5. 15 8 Think of 2 numbers that Multiply to 15 and Add to 8 3 x 5 = 15 3 + 5 = 8 3 5 Answer: (x + 3) (x + 5) Factor: x 2 + 8x + 15 c b #1#1 #2#2 add multiply

6. Multiplying integers Positive X Positive = Positive Positive X Negative = Negative Negative X Negative = Positive Adding Integers Positive + Positive = Positive Negative + Negative = Negative Positive + Negative = Subtract and take sign of bigger number Quick Review

7. 8 -6 Think of 2 numbers that Multiply to 8 and Add to -6 -4 x -2 = 8 -4 + -2 = -6 -4 -2 Answer: (x - 4) (x - 2) To check: Foil (x – 4)(x – 2) and see if you get x 2 -6x+8 Factor: x 2 - 6x + 8 c b #1#1 #2#2 add multiply

8. -9 8 Think of 2 numbers that Multiply to -9 and Add to 8 9 x -1 = -9 9 + -1 = 8 9 Answer: (x - 1) (x + 9) Factor: x 2 + 8x - 9 c b #1#1 #2#2 add multiply

9. Checkpoint Factor the expression. Factor x 2x 2 bx+c+ 1. x 2x 2 6x6x+5+ ANSWER () 1+x () 5+x 2. b 2b 2 7b7b+12+ ANSWER () 3+b () 4+b 3. s 2s 2 5s5s4+ – ANSWER () 4 – s () 1s – () 12+y () 1y – 4. y 2y 2 11y12 + – 5. x 2x 2 x+6 – ANSWER () 3+x () 2x –

10. means finding the values of x that would make the equation equal to 0. Solving ax 2 +bx+c = 0 Zero Product Property When the product of two expressions equals zero, then at least one of the expressions must equal zero. If AB = 0, then A = 0 or B = 0. If (x + 9)(x + 3) = 0, then x + 9 = 0 or x + 3 = 0. Example:

11. Solve the equation. - x 2x 2 +2x2x 15 = 0 SOLUTION = x 2x 2 +2x2x15 – 0 Factor. = 0 () 3x – () 5x + = 03x – or 5x + = 0 Use the zero product property. = 3xx = 5 – Solve for x. ANSWER The solutions are 3 and 5. – + 3 = + 3 - 5 = - 5 (mult) -15 2 (add) 5 -3

12. Solve the equation. x 2x 2 +9x9x = - 8 SOLUTION = x 2x 2 +9x9x8 + 0 Factor. = 0 () 8x + () 1x + = 08x + or 1x + = 0 Use the zero product property. = -8xx = 1 – Solve for x. ANSWER The solutions are -8 and -1. - 8 = - 8 - 1 = - 1 (mult) 8 9 (add) 8 1 Rewrite in standard form =x 2x 2 +9x9x -8

13. Checkpoint ANSWER 9, 1 Solve the equation. Solve a Quadratic Equation by Factoring ANSWER 7, 2 – 1. = x 2x 2 10x+9 – 0 2. = y 2y 2 5y5y+14 3. = x 2x 2 5 – 4x4x – ANSWER 5, 1 –

14. Homework 5.3 p.237 #18-42even.