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More lessons for factoring and other Grade 9 topics

*x*^{2} + 6*x* + 8

5*x*^{2} - 13 *x* + 6

**How to factor trinomials by grouping?**

Example:

Factor 12x^{2} + 34x + 10

**Factor trinomial by grouping**

Factor: 6x^{2} + 15x - 2

**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

You can use the free Mathway calculator and problem solver 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: *

*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: *

5

*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)

Example:

Factor 12x

Factor: 6x

Factor: -6x

Factor: 8x

Factor: 6x

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