Question

when searching factorization why do we list pairs of numbers with the correct product instead of pairs of numbers with the correct sum?

Answer 1

that is a very good question

Answer 2

Factors multiply to make products.
Factoring means to find numbers that multiply together.

Answer 3

maybe because if you are factoring over the integers, there are fewer of them

Answer 4

for example if i have
\[x^2-x-12\] and want to factor, i can think of tons of numbers that add to -1
\[1,-2\]\[2,-3\]\[3,-4\]\[4,-5\]\[5,-6\] etc etc