What adds to -6 and multiplies to -24?

Answer 1

Well since we're adding two numbers that result in a negative, and a product that is negative, we're looking for a positive and a negative number.

-24

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1 is prime

-12 x 2 = -24 = -10

-8 x 3 = -24 = -5

-6 x 4 = -24 = -2

5 doesn't make 24

4 x -6 = -24 = -2 (Uh oh, repeating multiplication)

Once you begin repeating multiplication you've found all possibilities that could result in the sum of -6 and the product of -24. However, since you've found no numbers to result in your desired sum/product, the trinomial in which you are factoring is prime.

Answer 2

The two numbers that add to -6 and multiply to -24 are -8 and 3. This can be determined by setting up a system of equations: x + y = -6 and x * y = -24. By solving these equations simultaneously, we find that x = -8 and y = 3 satisfy both conditions.