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Math Help - Polynomials and remainders

  1. #1
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    Post Polynomials and remainders

    Prove that when a polynomial f(x) is divided by ax + b, where a is not equal to 0 the remainder is f(-b/a).
    Find the polynomial in x of the third degree, which vanishes when x =-1 and x=2, has the value 8 when x=0 and leaves the remainder 16/3 when divided by 3x +2. someone please help me to figure this problem out. Thanks in advance.
    Last edited by mr fantastic; November 10th 2009 at 03:58 AM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by scrible View Post
    I have a log problem bothering me the question goes Prove that when a polynomial f(x) is divided by ax + b, where a is not equal to 0 the remainder is f(-b/a).
    Find the polynomial in x of the third degree, which vanishes when x =-1 and x=2, has the value 8 when x=0 and leaves the remainder 16/3 when divided by 3x +2. someone please help me to figure this problem out. Thanks in advance.
    Notice that a(-b/a)+b=0. If we divide f(x) by ax+b then there is some g(x) such that f(x)=g(x)(ax+b)+r(x), where r is the remainder. g(x) has a degree one less than f(x), so if f(x)=h*x^5+.... then g(x)=u*x^4_....

    f(x)=g(x)(ax+b)+r
    f(-b/a)=g(-b/a)(a(-b/a+b))+r
    f(-b/a)=g(-b/a)(0)+r
    f(-b/a)=r
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  3. #3
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    What do these have to do with logarithms?
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