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Math Help - Expanding triple brackets (easy?)

  1. #1
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    Expanding triple brackets (easy?)

    I'm gonna feel really dumb asking this but how do you expand triple brackets?

    I can do single and double brackets no problem with the FOIL method, but what multiplies with what when you have triple brackets?

    Also I was hoping you could help me on a question also here it is:

    <br />
x^3 - 2x^2 - 11x + 12 = 0

    I've deduced that (fx = 1) because 1^3 - 2 (1^2) - 11 (1) + 12 = 0<br />
    But what do I do next to factorise?

    Thanks in advance!
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  2. #2
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    Hello,

    Quote Originally Posted by Nick87 View Post
    I'm gonna feel really dumb asking this but how do you expand triple brackets?

    I can do single and double brackets no problem with the FOIL method, but what multiplies with what when you have triple brackets?

    Also I was hoping you could help me on a question also here it is:

    <br />
x^3 - 2x^2 - 11x + 12 = 0

    I've deduced that (fx = 1) because 1^3 - 2 (1^2) - 11 (1) + 12 = 0<br />
    But what do I do next to factorise?

    Thanks in advance!
    If \alpha is a root of a polynomial P(x) of degree n, then you can write : P(x)=(x-\alpha)Q(x), with Q(x) a polynomial of degree n-1.


    Here, you can write that x^3-2x^2-11x+12=(x-1)Q(x), where Q(x) is of degree 2 --------> Q(x)=ax^2+bx+c

    Try to find a,b & c
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  3. #3
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    x^3-2x^2-11x+12)\div(x-1)=x^2-x-12

    Now factor the quadratic x^2-x-12=0

    (x-4)(x+3)=0

    x=4 \ or \ x=-3

    Solutions {-3, 1, 4}

    Give an example of your triple bracket problem.
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  4. #4
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    Example of my triple bracket problem?

    I just need to PROVE that (x-1)(x-3)(x+2) = x^3 - 2x^2 - 5x + 6

    I know that it does because of the -3 and 2 being factors making the -2, -5 and +6 but i need to show expansion methods.

    By the way thanks Moo and Masters! Muchly helpful! :P
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  5. #5
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    First, expand the last two binomials using FOIL, since you know that method.

    (x-1)(x^2-x-6)

    Then, use the distributive property to multiply the binomial and the trinomial:

    x(x^2-x-6)-1(x^2-x-6)

    Continuing:

    x^3-x^2-6x-x^2+x+6

    Combine terms:

    x^3-2x^2-5x+6
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  6. #6
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    Thank you once again. My problem is solved!
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