What multiplies to -480 but adds to 4?

Answer 1

-476

Answer 2

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.