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Can you help with three problems 1)2x^2+7x+3 2)6x^2+5x-4 3)4x^2+12x+9 I have to factor this problems.Please help

  • math -

    What methods have you been taught?

  • math -

    FACTORING

  • math -

    What methods of factoring quadratic trinomials have you been taught ?

    Does decomposition ring a bell?

  • math -

    no

  • math -

    I will do the second one for you

    6x^2+5x-4

    multiply the first and last coefficients,
    6 x -4 = -24

    now look for 2 factors of -24 which have a sum of 5, the middle term coefficient.
    I think -3 and 8 will do it.
    so (-3)(8) = -24 and
    (-3) + (8) = 5

    so we will now "decompose" the middle term of 5x into -3x + 8x

    then 6x^2+5x-4
    = 6x^2 - 3x + 8x - 4
    Now factor it in pairs,
    = 3x(2x - 1) + 4(2x - 1)
    Notice that (2x - 1) is a common factor

    This must always happen!
    If you have found the combination for the multiplication and addition correctly you WILL HAVE A COMMON FACTOR
    so

    = (2x-1)(3x+4)

    There are other methods, but this one seems to be a common method taught these days. Although it might seem long, it is easy to understand and if factors exist, it will always work.

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