The first thing to do is find the factors of 6. These are 1, 2, 3 and 6. They can be paired up as 1 and 6, and 2 and 3. One of the numbers in the pair has to be negative, because they need to multiply to make -6. Also, because they need to sum to plus 1 (and one is negative) we need the factor pair that has a difference of 1. Thus the answer has to be 3 and -2.
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One such set is {-4, 5}.
a2+16 cannot be factored. There are no two numbers whose product is 16 and whose sum is 0.
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17 and 3 are two prime numbers whose sum is 20. Their product is 51.