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Thread: [SOLVED] Find the quotient and remainder in the division of polynomials.

  1. #1
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    [SOLVED] Find the quotient and remainder in the division of polynomials.

    It asks,
    for the following find polynomials q(x) and r(x) such that b(x) = q(x)a(x) + r(x) where r(x) =0 or deg r(x) < reg a(x),
    $\displaystyle 1. a(x) = x^2-2x+4, b(x)=2^5-x^4+3x^3-2x+1$

    What is it asking me to do? Does it want me to divide a(x) into b(x)? But then where do I get q(x) and r(x) from?

    I know how to do polynomials but I just don't understand what this question is asking me to do?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by driverfan2008 View Post
    It asks,
    for the following find polynomials q(x) and r(x) such that b(x) = q(x)a(x) + r(x) where r(x) =0 or deg r(x) < reg a(x),
    $\displaystyle 1. a(x) = x^2-2x+4, b(x)=2^5-x^4+3x^3-2x+1$

    What is it asking me to do? Does it want me to divide a(x) into b(x)?
    yes

    But then where do I get q(x) and r(x) from?
    q(x) is the quotient of the said division, r(x) is the remainder
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  3. #3
    MHF Contributor Reckoner's Avatar
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    Quote Originally Posted by driverfan2008 View Post
    It asks,
    for the following find polynomials q(x) and r(x) such that b(x) = q(x)a(x) + r(x) where r(x) =0 or deg r(x) < reg a(x),
    $\displaystyle 1. a(x) = x^2-2x+4, b(x)=2^5-x^4+3x^3-2x+1$

    What is it asking me to do? Does it want me to divide a(x) into b(x)? But then where do I get q(x) and r(x) from?

    I know how to do polynomials but I just don't understand what this question is asking me to do?
    If you divide $\displaystyle b(x)$ by $\displaystyle a(x),$ you will get a quotient and a remainder, both polynomials. Multiplying the divisor $\displaystyle a(x)$ by the quotient and adding the remainder should give the original dividend $\displaystyle b(x),$ and the provided equation has this form. Thus, $\displaystyle q(x)$ is the quotient and $\displaystyle r(x)$ the remainder when dividing $\displaystyle b(x)$ by $\displaystyle a(x).$
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  4. #4
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    Thanks very much Jhevon and Reckoner I understand now
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