Math

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Can someone please tell me Why is (4x + 5) (2x - 1) + (x - 9) (2x - 1) not in factored form? What is the correct final factored form? What is this factoring method called?

  • Math -

    If it is in factored form, it should have a common factor for the whole expression.

    (4x+5) is not a factor for the whole expression, just the first term (before the + sign).

    To factor "completely", we need to expand the expression, collect similar terms and factor from there.

    (4x + 5) (2x - 1) + (x - 9) (2x - 1)
    =8x²+6x-5 + 2x²-19x+9
    =10x²-13x+4
    =(5x-4)(2x-1)

  • Math -

    Or, note that (2x-1) is a common factor, so if you factor it out, you get

    (2x-1)(4x+5 + x-9) = (2x-1)(5x-4)

  • Math -

    Thanks, Steve!

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