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Math Help - Factoring Polynomials

  1. #1
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    Factoring Polynomials

    I have a test over factoring polynomials tomorrow. Most of it i have fairly well understood, but there's an extra credit section with problems we haven't discussed yet. I am not doing fantastic in math right now, so i could really use the bonus points. Can someone help explain them?

    Factor Completely. (Bi) (Bi)

    2x^2 - 7x - 4

    24x^2 + 47x - 2

    18c^4 - 3c^2 - 10

    16 - 9x + 15x^2

    Also, how can you determine in an answer in the format of (x + 1)(x - 2) whether it will be a +-, -+, ++, or -- answer?
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  2. #2
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    2x^{2}-7x-4

    (2x+1)(x-4)

    x=-\frac{1}{2} , x=4



    15x^{2}-9x+16

    b^{2}-4ac=<0 (less than 0, no roots)



    Also, how can you determine in an answer in the format of (x + 1)(x - 2) whether it will be a +-, -+, ++, or -- answer?
    Example

    2x^{2}-7x-4

    If the sign after '-7x' is negative, it means the signs within the two brackets will be different.
    ie. (2x + 1)(x - 4)

    If the sign was positive, it means the signs will be the same for both brackets. This sign used would be the sign after the squared term.
    ie. 12x^{2}-20x+3
    (2x - 3)(6x - 1)
    Last edited by r_maths; May 20th 2008 at 03:59 PM.
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  3. #3
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    Quote Originally Posted by Forkmaster View Post
    I have a test over factoring polynomials tomorrow. Most of it i have fairly well understood, but there's an extra credit section with problems we haven't discussed yet. I am not doing fantastic in math right now, so i could really use the bonus points. Can someone help explain them?

    Factor Completely. (Bi) (Bi)

    2x^2 - 7x - 4

    24x^2 + 47x - 2

    18c^4 - 3c^2 - 10

    16 - 9x + 15x^2

    Also, how can you determine in an answer in the format of (x + 1)(x - 2) whether it will be a +-, -+, ++, or -- answer?
    2x^2 - 7x - 4 = (2x +1)(x-4)

    24x^2 + 47x - 2 = (24x - 1)(x + 2)

    18c^4 - 3c^2 - 10 = (3c^2 + 2)(6c^2 - 5)

    16 - 9x + 15x^2 cannot be factored.

    And, to answer your final question, the way to tell ++ from -- is the middle term. Assuming the last term is positive: if the middle term is positive, then you have ++, and if the middle term is negative you have --. If the last term is negative, though, you just know that one of the roots will be positive and the other negative.
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  4. #4
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    +- is the same as -+ because AB = BA

    ++ when A, B and C are positive

    +- when A positive, C negative

    -- when A positive, B negative, C positive.

    2x^2 - 7x - 4 = (2x + 1)(x - 4)

    24x^2 + 47x - 2 = (24x - 1)(x + 2)

    18c^4 - 3c^2 - 10 = (6c^2 - 5)(3c^2 + 2)

    15x^2 - 9x + 16 has no real roots because 81 - 4*15*16 < 0
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