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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.

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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.

*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.

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