Make the given changes in the indicated examples of this section and then factor.

In Example 2(a), change the + before 7x to −.

Data from Example 2(a).

In order to factor x² + 7x − 8, we must find two integers whose product is −8 and whose sum is +7. The possible factors of −8 are

Inspecting these, we see that only +8 and −1 have the sum of +7. Therefore, x² + 7x − 8 = (x + 8)(x − 1)

In choosing the correct values for the integers, it is usually fairly easy to find a pair for which the product is the final term. However, choosing the pair of integers that correctly fits the middle term is the step that often is not done properly. Special attention must be given to choosing the integers so that the expansion of the resulting factors has the correct middle term of the original expression.

-8 and +1 +8 and -1 -4 and +2 +4 and -2