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Math Help - [SOLVED] Repeated factor?

  1. #1
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    [SOLVED] Repeated factor?

    There's this question that baffles me.

    Determine whether 2x - 3x + 1 has a repeated factor. If so, find the repeated factor.

    I used P(1) and found out that 2x - 3x + 1 = 0 when I substitute the 1 into x. Hence, I know that x - 1 is a factor of 2x - 3x + 1. But how do I know whether x - 1 is a repeated factor or not?
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  2. #2
    MHF Contributor Amer's Avatar
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    f(x)=2x^3-3x^2+1

    ok x-1 is a factor
    so by long divided I do not know what you call it you have

    (x-1)(2x^2-x-1)=2x^3-3x^2+1

    the right side is (2x+1)(x-1)so

    (x-1)(x-1)(2x+1)

    so you have repeated factor
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  3. #3
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    Oh, thank you! So I have factorise the quotient and see if one of the factor matches or not? But if I found 2 other factors since this is a cubic equation, does that mean I have to do 3 long divisions in order to see which one is a repeated factor? Or...are there any other less time-consuming way to find out the repeated factor? Thanks!
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  4. #4
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    You don't need to do long division. Just do synthetic division. For some examples as to how synthetic division works you could look at this thread:
    http://www.mathhelpforum.com/math-he...step-step.html


    01
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  5. #5
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    Quote Originally Posted by mark1950 View Post
    Oh, thank you! So I have factorise the quotient and see if one of the factor matches or not? But if I found 2 other factors since this is a cubic equation, does that mean I have to do 3 long divisions in order to see which one is a repeated factor? Or...are there any other less time-consuming way to find out the repeated factor? Thanks!
    There is one easy method, if you know differentiation. A root of a polynomial is a repeated root if it is also a zero of the differentiated polynomial.
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  6. #6
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    There is one easy method, if you know differentiation. A root of a polynomial is a repeated root if it is also a zero of the differentiated polynomial.
    Differentiating polynomials? Yea, I know differentiation and am wondering if it is much different that what I know. If you don't mind, can you please perform the example using this question:

    Determine whether 2x - 3x + 1 has a repeated factor. If so, find the repeated factor.

    Thank you very much!
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  7. #7
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    Quote Originally Posted by mark1950 View Post

    Determine whether 2x - 3x + 1 has a repeated factor. If so, find the repeated factor.

    Thank you very much!
    f(x)=2x^3-3x^2+1

    f(1)=0

    f'(x)=6x^2-6x

    f'(1)=0

    So 1 is a repeated root.

    2x^3-3x^2+1=(x-1)(x-1)(2x+1)
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  8. #8
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    Thanks. You guys are really much of help!
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