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Factoring Trinomials

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Working on how to factor trinomials, and the method that works best for me is the criss cross method, so Ive sticked with it. But Ive been stuck on one question for the past few minutes, and don't know what I've been doing wrong.

4x^2+23x+15

2x and 2x times to make a 4x. 5 and 3 times to make 15. And Im left with 10x and 6x, and they are supposed to add to make a 23x. But they are not:\ Ive even tried flipping them, but there's no point because the numbers are the same.

  • Factoring Trinomials -

    try
    (x-5)(4x-3)

  • Factoring Trinomials -

    Now to do that I solved the quadratic equation (google that)
    I found for solutions
    x = 5 and x = 6/8 which is 3/4
    so
    (x-5)(x-3/4) = 0 is solution
    I can multiply both sides by 4 to get rid of the faction
    (x-5)(4x-3) = 0

  • Factoring Trinomials -

    How did you get that using the criss cross method?

  • Factoring Trinomials -

    solving for zeros with quadratic equation:
    [ -23 +/- sqrt (529 - 240) ]/8

    [-23+/-17]/8

    -40/8 and -6/8

  • Factoring Trinomials -

    I never heard of the criss cross method. I used the quadratic equation to solve for zeros of the quadratic expression.

  • Factoring Trinomials -

    5 and 4 make 20
    1 and 3 make 3

  • Factoring Trinomials -

    Do it backwards from my solution and you will see :)

  • Factoring Trinomials -

    For the criss cross method, Im supposed to find two numbers that multiply to get 4x^2. And those were 2x and 2x. Then, Im supposed to find two numbers that multiply to give me 15, which was either 15 and 1 or 3 and 5. I used both, by criss crossing 2x to 3 and 2x to 5. That gave me 10x and 6x which does not give me 23x, and same with using 15 and 1, that just gave me 28, -28, etc.

  • Factoring Trinomials -

    Nevermind, I think I got it. Thanks for showing me the Quadratic way.

  • Factoring Trinomials -

    But 1 * 4 = 4 as well :)

  • Factoring Trinomials -

    b-6b+8

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