Factoring by Grouping Examples Page 1

Factor the polynomial y² + 35x + 7y + 5xy.

The first two terms don't have anything in common. Let's switch the middle two terms. If you can, see if you can do it without waking them. Those guys have had a long day and are all tuckered out.

We find

y² + 7y + 35x + 5xy

and now we can do our thing. The first two terms have a y in common, and the second two terms have 5x in common. We factor for

y(y + 7) + 5x(7 + y).

Since addition is commutative y + 7 = 7 + y, the previous line can be written as

y(y + 7) + 5x(y + 7).

Then we pull out the common factor of (y + 7) and get

(y + 5x)(y + 7).

Sometimes we have a choice of factors, positive or negative, and need to pick the negative one. We hate to be a negative Nancy, but there are instances in which it makes more sense than to be a positive Peter.