Factoring Quadratic Equations - Common Factors

The simplest way to factoring quadratic equations would be to find common factors. Sometimes, the first step is to factor out the greatest common factor before applying other factoring techniques.

In some cases, recognizing some common patterns in the equation will help you to factorize the quadratic equation. For example, the quadratic equation could be a Perfect Square Trinomial (Square of a Sum or Square of a Difference) or Difference of Two Squares.

In other cases, you will have to try out different possibilities to get the right factors for quadratic equations. This is still manageable if the coefficient of x² is 1. If the coefficient of x² is greater than 1 then you may want to consider using the Quadratic formula.

Printable & Online Algebra Worksheets

Factoring Out Common Factors

We can factorize quadratic equations by looking for values that are common.

Example:	x2 + 3x = 0
	We find that the two terms have x in common. We “take out” x from each term.
	x(x + 3) = 0
	We have two factors when multiplied together gets 0. We know that any number multiplied by 0 gets 0. So, either one or both of the terms are 0 i.e.
	x = 0 or x + 3 = 0 ⇒ x = -3       isolate variable x

This tells us that the quadratic equation x² + 3x = 0 can have two values (two solutions) for x which are x = 0 or x = –3

How to solve a quadratic equation by factoring out the greatest common factor?

Examples:
Solve
x² + 4x = 0
14x² - 35x = 0

• Show Video Lesson

Factoring and solving quadratic equations by factoring out the greatest common factor

Examples:
Solve
12x² + 18x = 0
4x² = 20x

• Show Video Lesson

How to factor and solve quadratic equations when the first step is to factor out the greatest common factor before apply other factoring techniques?

Examples:
Factor
5x² - 45 = 0
3x² - 6x - 45 = 0

• Show Video Lesson

Factoring Completely
The first step in all factoring problems is to check to see if a Greatest Common Factor can be factored out of the original polynomial.

Example:
Factor
3x² + 6x - 24

• Show Video Lesson

Factoring Out The Greatest Common Factor
To find the GCF of a polynomial

1. Write each term in factored form.
   
2. Identify the factors common to all terms.
   
3. Factor out the GCF.

Examples:
Factor out the GCF

1. 2x⁴ - 16x²
   
2. 4x²y³ + 20xy² + 12xy
   
3. -2x³ + 8x² - 4x
   
4. -y³ - 2y² + y - 7

• Show Video Lesson

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.