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.

**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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