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. Let's start adding up all the numbers that have a product of 70: 1 + (-70) = -69 -1 + 70 = 69 2 + (-35) = -33 -2 + 35 = 33 5 + (-14) = -9 Bingo! Since 5 + (-14) = -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) |