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: 1,-70 | -1,70 | 2,-35 | -2, 35 | 5, -14 | *bingo!* |
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 2*x*^{2} - 14*x* + 5*x* - 35 and factor: 2*x*(*x* - 7) + 5(*x* - 7) = (2*x* + 5)(*x* - 7) | |