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Math Help - indeterminate forms

  1. #1
    No one in Particular VonNemo19's Avatar
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    indeterminate forms

    Could someone justify the following statement please. I'm having trouble visualizing what has been said here:

    If by direct substitution of a given value c into a rational function is made and the following result occurs

    r(c)=\frac{p(c)}{q(c)}=\frac{0}{0}

    then it can be concluded that (x-c) is a factor of both p(x) and q(x).

    Anything to shed light here would be appreciated. Thanks.
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  2. #2
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    Quote Originally Posted by VonNemo19 View Post
    Could someone justify the following statement please. I'm having trouble visualizing what has been said here:

    If by direct substitution of a given value c into a rational function is made and the following result occurs

    r(c)=\frac{p(c)}{q(c)}=\frac{0}{0}

    then it can be concluded that (x-c) is a factor of both p(x) and q(x).



    Anything to shed light here would be appreciated. Thanks.
    if x = c is a zero of a function, then x-c is a factor.
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by VonNemo19 View Post
    Could someone justify the following statement please. I'm having trouble visualizing what has been said here:

    If by direct substitution of a given value c into a rational function is made and the following result occurs

    r(c)=\frac{p(c)}{q(c)}=\frac{0}{0}

    then it can be concluded that (x-c) is a factor of both p(x) and q(x).

    Anything to shed light here would be appreciated. Thanks.
    I am assuming p(x), q(x) are polynomials otherwise this does not make sense i.e

    \frac{\sin(\pi)}{\tan(\pi)}=\frac{0}{0} but neither have a factor of x-\pi

    The above is using the fact that

    If f is a polynomial and f(c)=0 then (x-c) divides f(x)

    example

    f(x)=x^2-3x+2 note that

    f(1)=1^2-3(1)+2=0 so by the above (x-1) divides x^2-3x+2 i.e this factors into f(x)=(x-1)(x-2)
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  4. #4
    No one in Particular VonNemo19's Avatar
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    I can kind of see that, but if you could explain why, I'd really appreciate it.
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Good stuff Empty dude. And yes of course they are polynomials. I kind of paraphrased what it said in the book. I'm no math writer.
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