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Easier way of factoring?

  1. Sep 5, 2013 #1
    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?
  2. jcsd
  3. Sep 5, 2013 #2


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    Staff: 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.
  4. Sep 5, 2013 #3


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    You had something like x^2 - 23x + 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.
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