Final answer:
There are no two numbers that both multiply to -96 and add up to -2, as confirmed by factoring and testing the sums of the factors of 96. Potential pairs of factors either don't add up to -2 or do not result in -96 when multiplied together.
Step-by-step explanation:
To determine whether there are possible numbers that multiply to -96 and add up to -2, we can set up a quadratic equation in the form ax^2 + bx + c = 0, where a and c are numbers that multiply to -96 (our c value), and b is the sum of these numbers (-2). In this case, we are looking for two numbers that multiply to c = -96 and also add up to b = -2. To find these numbers, we can perform factoring by finding two numbers that meet both criteria.
We know from the rules of multiplication that one number has to be positive and the other negative inorder to multiply to a negative number (-96 in this case). By listing the factors of 96 and testing their sums, we find that the two numbers that satisfy both conditions are -8 and 12 (since (-8) x 12 = -96 and (-8) + 12 = 4, which does not match our desired sum of -2).
Therefore, the answer is No, there are no two numbers that multiply to -96 and add up to -2.