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Math Help - Factorising explaination

  1. #1
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    Factorising explaination

    I've just been doing some revising and I came across a couple of factorisation questions that im not quite sure how to work out.

    x^4 - a6

    and

    x - x^5

    So if anyone could explain how to do them it would be really useful.
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  2. #2
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    Quote Originally Posted by Local_lunatic View Post
    I've just been doing some revising and I came across a couple of factorisation questions that im not quite sure how to work out.

    x^4 - a6

    and

    x - x^5

    So if anyone could explain how to do them it would be really useful.
    hello,

    I assume that you mean: x^4-a^6 . This is a difference of squares which can be factored to:

    x^4-a^6 = (x^2 - a^3)(x^2 + a^3)

    x-x^5 = x(1-x^4) . Factor out (?) the common factor. You get the result in the bracket by dividing each summand by the factor in front of the bracket:

    x-x^5 = x\left(\frac xx-\frac{x^4}{x}\right) = x(1-x^4)
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  3. #3
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    Quote Originally Posted by earboth View Post
    hello,

    I assume that you mean: x^4-a^6 . This is a difference of squares which can be factored to:

    x^4-a^6 = (x^2 - a^3)(x^2 + a^3)

    x-x^5 = x(1-x^4) . Factor out (?) the common factor. You get the result in the bracket by dividing each summand by the factor in front of the bracket:

    x-x^5 = x\left(\frac xx-\frac{x^4}{x}\right) = x(1-x^4)
    That's the answer I got for the second one too, but the book had a different one. Actually, the answer comes to the same thing it's just written differently.

    x(1+x^2)(1+x)(1+x)

    Which one am I meant to do in a test?
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  4. #4
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    Are you sure it doesn't say x(1+x^{2})(1+x)(1-x)? You wouldn't wanna make a typo like that on a test (I have done it before and lost 5 points for one sign so watch for it)
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  5. #5
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    Quote Originally Posted by Local_lunatic View Post
    That's the answer I got for the second one too, but the book had a different one. Actually, the answer comes to the same thing it's just written differently.

    x(1+x^2)(1+x)(1+x)

    Which one am I meant to do in a test?
    If the question asks you to factorise something full marks will be given
    for as complete a factorisation as possible under the constraints you
    are expected to observe (probably factors with real coefficients).

    RonL
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