x^2+7x-44. What factors of 44 have a difference of 7? 4*11=44 and 11-4=7.
So we have either (x-4)(x+7) or (x+4)(x-7). We have to make +7x so the plus sign has got to be in the same brackets as 7, the larger number, therefore the answer is (x-4)(x+7). (We have to have a minus in one bracket and a plus in the other so that the product has a minus sign, -44=-4*7.)