# Easier way of factoring?

Tyrion101
One of my quadratic formula problems required me to factor so that the product of 2050s factors added to -23, that may not be exact, but I basically asked for a new problem since it was just practice, after an hour of getting close but never the right answer, and I was wondering, other than just using the computer program I wrote (which would likely be cheating) is there anything that gets me an answer faster than just guessing factors?

Mentor
So you were supposed to find numbers a,b such that their product is 2050 and their sum is -23? That is not possible (at least not with real numbers).

Anyway, I would do it like that:
As a+b=-23, we can write b=-23-a.
Plug this into a*b=2050 and you get a regular quadratic equation. With the numbers in your post, it does not have solutions, but with other numbers it has.

Homework Helper
You had something like x^2 - 23x + 2050?

2050
2 - 1025
5 - 205
5 - 41
41 - 0

2050 is 2.5^2.41

Knowing the small primes helps. For example, I knew that 41 is prime. But also, there is an easy way to check. If a number n is composite, it has a prime factor ≤ ##\sqrt{n}##. So with 41, if it is composite, it has a prime factor < 7, so check 2,3,5, none divides it, so it is prime.