Factoring Trinomials By Grouping

Related Pages
Factoring Techniques
Factor Theorem
Solving Quadratic Equations
More Algebra Lessons
Grade 9 Math

When factoring trinomials by grouping, we first split the middle term into two terms. We then rewrite the pairs of terms and take out the common factor.

The following diagram shows an example of factoring a trinomial by grouping. Scroll down the page for more examples and solutions on how to factor trinomials by grouping.

• Factor Trinomials Worksheets

  Printable
  Factoring Trinomials (a = 1)
  Factoring Trinomials (a > 1)
  Factor Perfect Square Trinomials
  

  Factoring Quadratics (a = 1)
  Factoring Quadratics (a > 1)
  Factor Difference of Squares
  Factor Perfect Square Quadratics
  

  Online
  Factor Binomials by Difference of Squares
  Factor Perfect Square Trinomials
  
  Factor Trinomials or Quadratic Equations
  Factor Different Types of Trinomials 1
  Factor Different Types of Trinomials 2
  
  Solve Trinomials using Quadratic Formula
  Find Discriminants of Quadratic Polynomials

Example:
Factor the following trinomial using the grouping method.
x² + 6x + 8

Solution:
Step 1: Find the product ac:
(1)(8) = 8

Step 2: Find of two factors of 8 that add up to 6:
4 and 2

Step 3: Write 6x as the sum of 2x and 4x:
x² + 2x + 4x + 8

Step 4: Group the two pairs of terms:
(x² + 2x) + (4x + 8)

Step 5: Take out the common factors from each group:
x(x + 2) + 4(x + 2)

Step 6: Since the two quantities in parentheses are now identical. That means we can factor out a common factor of (x + 2):
(x + 4)(x + 2)

Example:
Factor the following trinomial using the grouping method.
5x² - 13 x + 6

Solution:
Step 1: Find the product ac:
(5)(6) = 30

Step 2: Find of two factors of 30 that add up to 13:
3 and 10

Step 3: Write -13x as the sum of -3x and -10x:
5x² - 3x - 10x + 6

Step 4: Group the two pairs of terms:
(5x² - 3x) - (10x + 6)

Step 5: Take out the common factors from each group:
x(5x - 3) - 2(5x - 3)

Step 6: Since the two quantities in parentheses are now identical. That means we can factor out a common factor of (x - 2):
(x - 2)(5x - 3)

How to factor trinomials by grouping?

Example:
Factor 12x² + 34x + 10

• Show Video Lesson

Factor Trinomial By Grouping
Factor: 6x² + 15x - 21

• Show Video Lesson

Factor Trinomial, GCF And Then Grouping Method
Factor: -6x² + 60x - 28

• Show Video Lesson

Factoring Trinomials: The Grouping Method
Factor: 8x² + 35x + 12

• Show Video Lesson

How to factor Trinomials using GCF and the Grouping Method?
Factor: 6x² - 3x - 45

• 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.