Recognizing Products Examples Page 2

Factor the polynomial 8x² - 56x + 98.

The terms have a common factor of 2, so the first thing we do is pull that out to get

2(4x² - 28x + 49).

Now we need to factor the part in parentheses if possible. Since the middle term has a negative sign, we hope we can factor this part as

(▲)² - (■)².

We would need

▲ = 2x

and

■ = 7.

Squaring (2x - 7) does give us 4x² - 28x + 49, so we can factor the original polynomial as

2(2x - 7)².

This result was so much more satisfying than that of the last example. Like the last bite of a slice of banana cream pie. Actually, more like the first bite, because then there are still all those other bites left.