Math

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factor the polynomials using whatever strategy seems appropriate.
12m^2n^2-8mn+1

  • Math -

    Just by inspection,

    (2mn-1)(6mn-1)

  • Math -

    How did you get that?

  • Math -

    Think of it like factoring

    12x^2 - 8x + 1
    or
    x^2 - 8x + 12

    You want factors of 12 that add to 8

    That'd be 6 and 2.

    It takes some experience to get quick at factoring by inspection. Do lots of these till you don't have to spend a lot of time guessing.

    If the middle term is small, and the last term is negative, you want factors that are close to each other:

    (x^2-4x+96) = (x-12)(x+8)

    If the middle term is positive, it's easier to imagine factors that add up.

    Of course, if you are faced with something like

    (12x^2 - 29x + 60)

    you will have lots of possible combinations.

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