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Math Help - Trinomial factoring help

  1. #1
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    Trinomial factoring help

    Hello,

    I have been learning how to factor trinomials and I am stuck..

    2x^2+x-15 = (2x-5)(x+3)

    3a^2-2a-5 = (3a-5)(a+1)

    Fc^2+17c+14 = (fc+7)(c+2)

    To factor these types of problems, is the only way real to just plug in factors and do a full test with foil?? I mean some of these could have 100 possible factor pairs.. do you have to plug them in and keep going until it works? Am I missing a shortcut?


    thanks!
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  2. #2
    Member Jonboy's Avatar
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    when you start out learning factoring you normally do it the harder way.

    but there's some logic with factoring.

    given ax^2 + bx + c, if the a is greater than one, you can do what's called the AC method.

    For 2x^2{\color {blue}{+x}}-15 you first multiply the a and c.

    That's -30. Since the linear term has a coefficient of +1, you need to find two numbers that multiply to give you -30 and add up to 1.

    That's 6 and -5.

    So rewrite this as: 2x^2 + 6x -5x - 15

    Notice how I keep the -5x near the -15 since they have a common term.

    Pull out a greatest common factor between terms: 2x(x + 3) -5(x + 3)

    Factor by grouping: \boxed{(2x - 5)(x + 3)}

    I might've went too fast, but we'll explain something more detailed if you ask the question.
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  3. #3
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    Pull out a greatest common factor between terms:

    Factor by grouping:

    will you always get a similar as in the (X+3) in the part? what happens if its different, or will it not be different?

    thanks
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  4. #4
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    You can just use the quadratic formula to factor trinomials. You may find this easier.

    For example, factor 2x^{2}+x-15.

    Use quadratic formula,
    x= {\dfrac{-b \pm \sqrt{b^{2}-4ac}}{2a}} = {\dfrac{-(1) \pm \sqrt{(1)^{2}-4(2)(-15)}}{2(2)}}.

    So x = -3 or x=\frac{5}{2}.

    Now take x = -3 and add 3 to both sides of the equation to get: (x+3)=0.

    Now take x=\frac{5}{2} and multiply both sides of the equation by 2 to get 2x=5. Then subtract both sides by 5 to get (2x-5)=0.

    Multiplying the two quantities,
    (2x-5)(x+3)=0

    And you're done.
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  5. #5
    Member Jonboy's Avatar
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    Hey I never thought of that before! That was spectacular Pn0yS0ld13r
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  6. #6
    Member Jonboy's Avatar
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    Quote Originally Posted by blip911 View Post
    Pull out a greatest common factor between terms:

    Factor by grouping:

    will you always get a similar as in the (X+3) in the part? what happens if its different, or will it not be different?

    thanks
    it might be different sometimes, you'll have to group the terms differently.
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