# Factor Trinomials by Grouping

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More lessons for factoring and other Grade 9 topics

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.

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
Factor trinomial by grouping
Factor: 6x2 + 15x - 2
Factor trinomial, gcf and then grouping method
Factor: -6x2 + 60x - 28
Factoring Trinomials: The Grouping Method
Factor: 8x2 + 35x + 12
How to factor Trinomials using GCF and the Grouping Method?
Factor: 6x2 - 3x - 45

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