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Math Help - Division & Remainder of Polynomials - please need help

  1. #1
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    Division & Remainder of Polynomials - please need help

    Hi this is the question, I have no idea how to solve it so help would be appreciated.

    Q: When a polynomial is dived by (2x+1)(x-3), the remainder is 3x -1. What is the remainder when the polynomial is divided by 2x + 1?

    Please, help would be tremendously appreciated. Please show working out, and WHY you must do that working out.

    Thank you very much everyone.
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  2. #2
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    Quote Originally Posted by SeaNanners View Post
    Hi this is the question, I have no idea how to solve it so help would be appreciated.

    Q: When a polynomial is dived by (2x+1)(x-3), the remainder is 3x -1. What is the remainder when the polynomial is divided by 2x + 1?

    Please, help would be tremendously appreciated. Please show working out, and WHY you must do that working out.

    Thank you very much everyone.
    Just have a think about this.

    The polynomial has a remainder 3x-1 when divided by (2x+1)(x-3)

    If P(x)=(2x+1)(x-3)(3x-1)

    and you divide that by (2x+1)(x-3), what will the answer be ?
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  3. #3
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    [QUOTE=Archie Meade;580044]Just have a think about this.

    The polynomial has a remainder 3x-1 when divided by (2x+1)(x-3)

    If P(x)=(2x+1)(x-3)(3x-1)

    No, but 3x-1 is the remainder not a factor. So P(x) = Q(x).(2x+1)(x-3) + 3x -1. The question is asking what is the remainder if it is P(x)/2x+1, so P(x)=Q(x).(2x+1) + ......... Now the ......... is what must be found. I know its something to do with the remainder theorem but I don't know how to use it.

    Thanks anyways.
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  4. #4
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    That remainder! sorry!

    \displaystyle\frac{P(x)}{(2x+1)(x-3)}=A(x)+\frac{3x-1}{(2x+1)(x-3)}

    \displaystyle\frac{P(x)}{(2x+1)}=\frac{P(x)[x-3]}{(2x+1)[x-3]}=A(x)[x-3]+\frac{(3x-1)[x-3]}{(2x+1)(x-3)}

    same remainder!
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