In these lessons, we will learn to factor 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.
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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.
x^{2} + 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:
x^{2} + 2x + 4x + 8
Step 4: Group the two pairs of terms:
(x^{2} + 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.
5x^{2} - 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:
5x^{2} - 3x - 10x + 6
Step 4: Group the two pairs of terms:
(5x^{2} - 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 12x^{2} + 34x + 10
Factor Trinomial By Grouping
Factor: 6x^{2} + 15x - 21
Factor Trinomial, GCF And Then Grouping Method
Factor: -6x^{2} + 60x - 28
Factoring Trinomials: The Grouping Method
Factor: 8x^{2} + 35x + 12
How to factor Trinomials using GCF and the Grouping Method?
Factor: 6x^{2} - 3x - 45
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