4.6 Solving Quadratic Equations by Factoring BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 Solving Quadratic Equations by Factoring The Multiplication Property of Zero says that zero multiplied by any number is zero. Examples: 4  0 = 0, 0  (– 32) = 0, a  0 = 0 where ‘a’ is any real number Zero Product Rule: For real numbers a and b: if ab = 0, then a = 0 or b = 0. Solution: Using the Principle of Zero Products, set each factor equal to 0 and solve each equation. x = 0 or x + 8 = 0 x = –8 Answer: Your Turn Problem #1

4.6 Solving Quadratic Equations by Factoring BobsMathClass.Com Copyright © 2010 All Rights Reserved. 2 The equation must be in factored form with 0 on one side to utilize the Zero Product Rule. 1 st, get 0 on the right hand side by subtracting 28x from both sides. 2 nd, factor the left hand side. 3 rd, set each factor equal to zero and solve each equation. Answer: Your Turn Problem #2

4.6 Solving Quadratic Equations by Factoring BobsMathClass.Com Copyright © 2010 All Rights Reserved. 3 Procedure: Factoring Equations and Using the Zero Product Rule Step 1. If the problem is already factored, and there is a zero on one side of the equation, we can use the Zero Product Rule (i.e. set factors equal to zero and solve). Step 2.If the problem is not factored or does not have a zero on one side of the equation, then:a. Multiply any products of polynomials. b. Bring all terms to one side only and collect like terms. c. Rearrange into standard form (descending order). d. Factor Completely. e. Use the Zero Product Rule. Two conditions must be met before we can use the Zero Products Rule. Zero must be on one side, which it already is. It also must be completely factored, which it is not. Solution: Your Turn Problem #3 Now, we can use the zero product rule.

4.6 Solving Quadratic Equations by Factoring BobsMathClass.Com Copyright © 2010 All Rights Reserved The first step is to get zero on the RHS. Solution: 3. Use the Zero Product Rule. 2. Factor completely. Your Turn Problem #4

4.6 Solving Quadratic Equations by Factoring BobsMathClass.Com Copyright © 2010 All Rights Reserved. 5 Solution: Although the left-hand side is factored, zero is not on one side. Therefore, our goal is: 1. Multiply the left-hand side. 2.Bring all the terms to one side. 3.Rearrange into standard form 4.Factor. 5.Use Zero Product Rule. Your Turn Problem #5

4.6 Solving Quadratic Equations by Factoring BobsMathClass.Com Copyright © 2010 All Rights Reserved. 6 There is already a zero on the RHS. We can then factor completely and use the the zero product rule. There is no solution for this factor since there is not a real number solution for this equation. The x 2 – 4 can be factored since it is the difference of two squares. However the x 2 +9 can not be factored since there is no formula for the sum of two squares. Your Turn Problem #6 The End B.R