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Thread: Polynomial Division

  1. #1
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    Polynomial Division

    if a is in Q how would i show that f(a) is the remainder after dividing the polynomial f(x) by (x-a)?
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  2. #2
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    Quote Originally Posted by stephanderson View Post
    if a is in Q how would i show that f(a) is the remainder after dividing the polynomial f(x) by (x-a)?
    If $\displaystyle f(x)$ is a polynomial of degree $\displaystyle n $ in $\displaystyle x$, dividing by $\displaystyle (x-a)$ leaves a quotient $\displaystyle G(x)$ of degree $\displaystyle n-1$ with remainder $\displaystyle R$ (a constant). That is $\displaystyle f(x) = (x-a)g(x)+R$. If you put $\displaystyle x = a$, you will get $\displaystyle f(a) = R$.
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