This problem involves finding two integers that have the specified product and sum for each case.

Let’s walk through a few of them to understand how to solve them mentally:

a) Product = 4, Sum = 4

We need two integers whose product is 4 and whose sum is 4. The possible integer pairs that multiply to 4 are:

• (1, 4)
• (-1, -4)
• (2, 2)

Among these, the pair that adds up to 4 is (0, 4).

b) Product = 6, Sum = 5

We need two integers whose product is 6 and whose sum is 5. The pairs for the product of 6 are:

• (1, 6)
• (-1, -6)
• (2, 3)
• (-2, -3)

The pair that adds up to 5 is (1, 6).

If you'd like to solve more or need further clarifications on any specific pair, feel free to ask! Would you like to solve more of the problems, or would you like me to continue working through these examples?

Here are some related questions for practice:

1. How would you approach solving for a product of negative numbers with a positive sum?
2. Can you think of another way to use algebra to solve these problems instead of guessing pairs?
3. What happens if the sum is negative, but the product is positive?
4. How would you handle large numbers or negative products in this type of problem?
5. Can you generalize a rule for solving these problems efficiently?

Tip: To solve this quickly, try factoring the product and checking the sum of the factors systematically!