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List all the pairs of integers with a product of -42. Then find the pair whose sum is -19.

Select all that apply:

A. -1 and -42
B. -7 and 6
C. -1 and 42
D. -3 and 14
E. 1 and 42
F. 3 and -14
G. 1 and -42
H. -2 and 21
I. 2 and -21
J. 7 and -6

Answer :

To solve the problem, we need to list all pairs of integers whose product is -42 and then find which of those pairs has a sum of -19.

### Step 1: Find Pairs with a Product of -42
To find pairs of integers that multiply to -42, we consider combinations of factors of 42. Since the product is negative, one of the numbers must be negative.

Here are the factor pairs of 42:
- 1 and 42
- 2 and 21
- 3 and 14
- 6 and 7

Because we want the product of the pairs to be -42, we'll make one number in each pair negative:

1. -1 and 42 (and its reverse: 1 and -42)
2. -2 and 21 (and its reverse: 2 and -21)
3. -3 and 14 (and its reverse: 3 and -14)
4. -6 and 7 (and its reverse: 6 and -7)

### Step 2: Check for Pairs Whose Sum is -19
Now, we'll check each pair to see if their sum equals -19:

- Pair (-1, 42): Sum = -1 + 42 = 41
- Pair (1, -42): Sum = 1 + (-42) = -41
- Pair (-2, 21): Sum = -2 + 21 = 19
- Pair (2, -21): Sum = 2 + (-21) = -19
- Pair (-3, 14): Sum = -3 + 14 = 11
- Pair (3, -14): Sum = 3 + (-14) = -11
- Pair (-6, 7): Sum = -6 + 7 = 1
- Pair (6, -7): Sum = 6 + (-7) = -1

The pair that has a sum of -19 is (2, -21).

### Conclusion
The pair of integers with a product of -42 and a sum of -19 is 2 and -21.

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