8.3 Factoring Quadratic Equations Objective The student will be able to: Factor trinomials with grouping. Solve quadratic equations using Zero Product Property.

Factoring Chart This chart will help you to determine which method of factoring to use. TypeNumber of Terms 1. GCF 2 or more 2. Grouping 4 3.Quadratic 3 Trinomials

First terms: Outer terms: Inner terms: Last terms: Combine like terms. y 2 + 6y + 8 y2y2 +4y +2y +8 Review: (y + 2)(y + 4) In this lesson, we will begin with y 2 + 6y + 8 as our problem and finish with (y + 2)(y + 4) as our answer.

Ex1) Factor: y 2 + 6y + 8 Use your factoring chart.

Ex 1) Factor y 2 + 6y + 8 MultiplyAdd Product of the first and last coefficients Middle coefficient Here’s your task… What numbers multiply to +8 and add to +6? If you cannot figure it out right away, write the combinations. M A

Ex 1) Factor y 2 + 6y + 8 Place the factors in the table. +1, +8 -1, -8 +2, +4 -2, -4 MultiplyAdd Which has a sum of +6? +9, NO -9, NO +6, YES!! -6, NO We are going to use these numbers in the next step!

Ex 2) Factor x 2 – 2x – 63 MultiplyAdd Product of the first and last coefficients Middle coefficient -63, 1 -1, , 3 -3, 21 -9, 7 -7, Signs need to be different since number is negative. M A

Replace the middle term with our working numbers. x 2 – 2x – 63 x 2 – 9x + 7x – 63 Group the terms. (x 2 – 9x) (+ 7x – 63) Factor out the GCF x(x – 9) +7(x – 9) The parentheses are the same! Weeedoggie! (x + 7)(x – 9)

4 steps for solving a quadratic equation 1.Set the equation equal to 0. 2.Factor the equation. 3.Set each part equal to 0 and solve. 4.Check your answer on the calculator. Set = 0 Factor Split/Solve Check

Ex 3) Solve: – 24a +144 = – a 2 Put it in descending order. a 2 – 24a = 0 (a – 12) 2 = 0 a – 12 = 0 a = 12 {12} Set = 0 Factor Split/Solve Check

Ex 4) Solve: x 3 + 2x 2 = 15x x 3 + 2x 2 – 15x = 0 x(x 2 + 2x – 15) = 0 x(x + 5)(x – 3) = 0 x = 0 or x + 5 = 0 or x – 3 = 0 {0, – 5, 3} Set = 0 Factor Split/Solve Check

8.3 HW PG. 489 #13 – 29 ODDS (9 PROBLEMS)

Here are some hints to help you choose your factors in the MAMA table. 1) When the last term is positive, the factors will have the same sign as the middle term. 2) When the last term is negative, the factors will have different signs.