Zero Product Property If ab = 0, then ???If ab = 0 then either a = 0 or b = 0 (or both).If the product 0f two numbers is 0, then at least one of the factors must be zero!
Solving by Factoring Investigation Click the link belowUsing Factoring to Solve Return here when done for more practice.
Solving Using the Zero Product Property Solve (x - 1)(x - 3) = 0If two factors multiply to be zero then at least one factor must be equal to zero! So… x - 1 = 0 or x - 3 = 0 Solve each equation…. x = 1 or x = 3
When you need to factor first… Solve x2 –2x - 8 = 0.Step 1: Factor : x2 – 2x – 8 = (x – 4)(x + 2) (x – 4)(x + 2) = 0Step 2: Set each factor equal to zero. x – 4 = 0 or x + 2 = 0Step 3: Solve: x = 4 or x = -2
When it’s not equal to zero…. Solve x2 + 5x + 6 = 20. You must set it equal to zero first! x2 + 5x + 6 -20= 20-20 x 2 + 5 x - 14= 0 Now you can factor and solve….
Step 1: Factor (x + 7)(x – 2) = 0Step 2: Set each factor equal to zero. x + 7 = 0 or x – 2 = 0Step 3: Solve: x = –7 or x = 2
Suppose you are trying to create a garden.The length of the garden needs to be six feet longer than the width. You will be given 40 square feet of space. What are the dimensions of the garden? We know that the length is (x + 6) and the width is (x). The area is 40 sq. ft.If area equals l times w, then (x)(x+6) = 40.We want to find the values that make this equation true.We are going to use factoring to help solve this problem.
Let’s solve our garden problem! What are the dimensions of the garden? (x)(x+6) = 40 Simplify First: x2 + 6x = 40 Set equal to zero: x2 + 6x – 40 = 0 Factor the equation completely. (x + 10)(x-4) = 0 Set each factor equal to zero, and solve. x- 10 = 0 therefore x = -10 x – 4 = 0 therefore, x = 4 Can the width be two values at once? Which solution do we choose?
You can’t have a negative length!x = -10 does not make sense in the context of the problem, it cannot be an answer. Consequently, x = 4 Plug in 4 for x and find the width. The dimensions are 4 ft and 10 feet.
More Examples… Solve; x 2 -4x = 5Set the equation equal to zero. x2 - 4x – 5 = 0Factor the left side of the equation (x - 5)(x + 1) = 0Use the Zero Product PropertyIf I multiply the two expressions on theleft and product is equal to zero, (x - 5)= 0 or (x + 1) = 0one of the two must be equal to zero.Set each linear factor equal to zero. x - 5 = 0 or x + 1 = 0Solve each equation x = 5 x = -1
View the following videos for areview of solving by factoring. Click Here for Additional Explanation