Factoring by Grouping Examples Page 3

Factor by grouping: 2x² - 9x - 35.

Here we need two numbers whose product is -70 and whose sum is -9 (don't forget those negative signs). To have a product of -70, exactly one of the numbers must be negative. We don't care which one, as long as somebody volunteers.

Numbers that have a product of 70:

Since -14 + 5 = -9, we can stop looking at factors of 70 now. Good, because our eyes were starting to zone out a bit.

We rewrite the original polynomial as

2x² - 14x + 5x - 35

and factor:

2x(x - 7) + 5(x - 7) = (2x + 5)(x - 7)