Question

#1. Factor the expression. 4g^2+21g-49

Answer 1

1. You want to find factors of 4×(-49) that add to 21. Those would be +28 and -7. Replacing the term 21g with the sum 28g -7g, we get an expression that can be factored by grouping.

... (4g² +28g) + (-7g -49)

... = 4g(g +7) -7(g +7) = (4g-7)(g+7)

2. After you factor out 5, you have 5(64y² -16y -15). As in the previous problem, you're looking for factors of 64×(-15) = -960 that sum to -16. There are 14 factor pairs of 960, so it can take a little bit of effort to find the right pair. That pair is -40 and 24. As in the previous problem you replace the term -16y with the sum -40y +24y and factor by grouping.

... = 5(64y² -40y +24y -15) = 5(8y(8y -5) +3(8y -5))

... = 5(8y +3)(8y -5)

3. False. It is perhaps easiest to check this by multiplying out the offered factors. Doing that gives you 36k² -36k +8k -8. The collected k terms add to -28k, not -44k.