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Math

Attribution

Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in October 2020. This work is licensed under a Creative Commons BY 4.0 International License.

Factoring Quadratic Equations

One way to solve a quadratic equation is by factoring the equation. A general quadratic equation is given by:

                                                    

In order to factor a quadratic equation, one has to perform the following steps:

 

Step 1) Find two numbers whose product is equal to ac, and whose sum is equal to b.
Step 2) Write the middle term, bx, as the sum of two terms. The coefficients of the two terms are the two numbers found in Step 1).
Step 3) Factor the first two terms and the second two terms separately. 
Step 4) Factor the common term and set different factors equal to zero and solve for the variable.

 

Example: Solve  by factoring.

 

Step 1) We look for two numbers whose product is 63 and whose sum is -16. Those two numbers are -9 and -7.
Step 2) We rewrite the quadratic equation as:

Step 3) We factor the first two terms and the second two terms separately:

Step 4) We factor the equation and solve:

 

Example: Solve  

 

Step 1) We have to find two numbers whose product is 9 and whose sum is 6. Those two numbers are 3 and 3.
Step 2) We rewrite the equation as:

Step 3) We factor the first two terms and write the second two terms separately:

Step 4) We factor the equation and solve:

 

Example: Solve 

 

Step 1) Two numbers that multiply to give -30 and add to give 1 are 6 and -5.
Step 2) Using the numbers from step 1), we rewrite the equation as:

Step 3) We group every two terms and factor them:

Step 4) We factor the equation and solve:

 

 

 

 

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