Example 5

Write the trinomial as a product of factors.

Step 1: If possible, identify the GCF.

The GCF is 3.

Step 2: Find a pair of numbers with a product of ac (2 × −7 = −14 in this case) and a sum of b (−13 in this case) .

Note the trinomial that must now be factored is . However, do not forget about the GCF of 3. It must be carried through as a factor to the very end.

first number second number product sum
1
−14
−14
−13
−1
14
−14
13
2
−7
−14
−5
−2
7
−14
5

Step 3: The numbers 1 and −14 add to −13 and multiply to −14. Rewrite the middle term (b-term) as two terms with coefficients 1 and −14.

Step 4: Group the first two terms and the last two terms.

Step 5: Remove the greatest common factor from each of the two groups.

Step 6: The result is a common factor, , in each group. Remove the common factor and simplify.

You have now factored the trinomial into its three factors. Don't forget about the GCF of 3.