Solving Equations by Factoring
Examine the equation below: ab = 0
If you let a = 3, then logically b must equal 0. Similarly, if you let b = 10, then a must equal 0.
Now try letting a be some other non-zero number. You should observe that as long as a does not equal 0, b must be equal to zero.
To state the observation more generally, "If ab = 0, then either a = 0 or b = 0." This is an important property of zero which we exploit when solving by factoring.
0 is our magic number because the only way a product can become 0 is if at least one of its factors is 0.
When the example is factored into (x - 2)(x - 3) = 0, this property was applied to determine that either (x - 2) must equal zero, or (x - 3) must equal zero. Therefore, we are able to create two equations and determine two solutions from this observation.
Remark:
You can’t guarantee what the factors would have to be if the product was set equal to any other number. For example if ab = 1, then a = 5 and b = 1/5 or a = 3 and b = 1/3, etc. But with the product set equal to 0, we can guarantee finding the solution by setting each factor equal to 0.
To learn more about solving equations by factoring
Solving Equations by Factoring
Practice: Solve equations by factoring and by using the Zero Product Property in the following exercises.
Solving Equations by Factoring 1