Solving Quadratic Equations by Factoring

Today we are going to learn how to find a root of a quadratic equation by factoring.

In a previous lesson we learned that the standard form of a quadratic equation is:

ax² + bx + c = 0 

The roots of a quadratic equation are the solutions to the equation.  Take for example the following equation:

x² − 3x + 2

We need to find 2 numbers whose product is 2 and sum is -3.  What are those numbers?  -1 and -2.

Plug the two numbers into the following equation:

(x +  ) (x +   )


(x - 1) (x - 2)

Set each equation equal to zero to find the roots.

x - 1 = 0

x = 1

x - 2 = 0

x = 2

So, the roots are 1 and 2.

A double root occurs when the two roots are equal. Here's an example:

x² − 12x + 36

Can be factored as (x - 6) (x - 6)

If x = 6, then each factor will be 0, and therefore the quadratic will be 0.  6 is called a double root.

Practice Problems

Solve each of the following equations by factoring.  Remember to show your work!  Turn in your completed worksheet in class tomorrow.


1. x² + 7x + 12

2. x² + 3x − 10

3. x² − 3x + 2

4. 2x² + 7x + 3 

5. x² − 2x + 1

6. x² − x − 30

7. x² + 12x + 36

8. 3x² + x − 2

Need more practice?  Take this online factoring quiz