Factor Trinomials by Grouping

When factoring trinomials by grouping, we first split the middle term into two terms. We then rewarite 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)

The following videos show how to factor trinomials by grouping.

Factor trinomial by grouping

Factor trinomial by gcf then grouping method

factor trinomial, gcf then grouping

factor trinomial by gcf then grouping

Custom Search