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The numbers are: 24 and -20
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This is part of the routine of factoring trinomials. You get better at it with practice, but if you haven't yet developed the x-ray vision to see the answer right away, you can "crank it out" like this:
First, find the prime factorization of 480: = 2x240 = 2x2x120 = 2x2x2x60 = 2x2x2x2x30 = 2x2x2x2x2x15 = 2x2x2x2x2x3x5.
Now, list all possible pairs of factors of 480 - the factorization above should help.
2, 240
3, 180
4, 120
5, 96
6, 80
8, 60
10, 48
12, 40
15, 32
16, 30
20, 24
24, 20 ... whoops, we already have that, so we can stop here.
We look at the difference of the factors, since we are factoring a negative number. Obviously, 20 and 24 are what we need. Since we need a positive sum, make the big one positive: +24 and -20.
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What adds up to -52 and multiplies to -480?
8 and -60
What adds to 5 but multiplies to 4?
4 1
What multiplies to -60 but adds to 4?
-56
What adds to 28 and multiplies to 4?
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4
What adds to get 5 and multiplies to get -4?
1
What multiplies to 24 and adds to -4?
20
What multiplies to -12 and adds up to -4?
-16
What multiplies to 44 and adds to 15?
4 and 11.
What adds to get 9 and multiplies to get 20?
4 and 5
What adds to -4 and multiplies to -4?
-8
What is multiplies to 20 but adds to 4?
24
What multiplies to 3 and adds to 4?
7
