Related Topics:

More lessons for factoring and other Grade 9 topics

Factor trinomial by GCF then grouping method.
Factor trinomial, GCF then grouping.

actor trinomial by GCF then grouping.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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.

*x*^{2} + 6*x* + 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 6*x* as the sum of 2*x* and 4*x*:

*x*^{2} + 2*x* + 4*x* + 8

**Step 4:** Group the two pairs of terms:

(*x*^{2} + 2*x*) + (4*x* + 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.

5*x*^{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 -13*x* as the sum of -3*x* and -10*x*:

5*x*^{2} - 3*x* - 10*x* + 6

**Step 4:** Group the two pairs of terms:

(5*x*^{2} - 3*x)* - (10*x* + 6)

**Step 5**: Take out the common factors from each group:

*x*(5*x* - 3) - 2(5*x* - 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)(5*x* - 3)

The following videos show how to factor trinomials by grouping.

Factor trinomial by groupingactor trinomial by GCF then grouping.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other 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.