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Math Help - tricky remainder of the polynomial

  1. #1
    rcs
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    tricky remainder of the polynomial

    remainder if ((5x+10)^2012)+ 4 divided by x+2

    can anyone help me on this please
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: tricky remainder of the polynomial

    Theres a theorem that says that, the remainder of Any polynomial divded by a linear factor,  a_n x^n +...+a_0 divided by  x - a the remainder is f(a).

    For example,  x^3 + x^2 + 3 divided by  x+ 3 = x - -3, the remainder is  f(-3)= (-3)^3 + (-3)^2 + 3 = 21
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  3. #3
    rcs
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    Re: tricky remainder of the polynomial

    Quote Originally Posted by jakncoke View Post
    Theres a theorem that says that, the remainder of Any polynomial divded by a linear factor,  a_n x^n +...+a_0 divided by  x - a the remainder is f(a).

    For example,  x^3 + x^2 + 3 divided by  x+ 3 = x - -3, the remainder is  f(-3)= (-3)^3 + (-3)^2 + 3 = 21


    if that is what im going to do, then

    [5(-2) + 10]^2012 + 4
    [-10 + 10]^2012 + 4
    0 + 4
    meaning 4 is the remainder

    is this correct sir?
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: tricky remainder of the polynomial

    Did you know that (5x+10)=5(x+2)?

    Can you rewrite ((5(x+2))^2012)+ 4?
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  5. #5
    rcs
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    Re: tricky remainder of the polynomial

    Quote Originally Posted by ILikeSerena View Post
    Did you know that (5x+10)=5(x+2)?

    i know above, but below , well i cant, Can you?

    Can you rewrite ((5(x+2))^2012)+ 4?
    so that it makes things easier now.

    thanks
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  6. #6
    Senior Member jakncoke's Avatar
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    Re: tricky remainder of the polynomial

    Yes remainder is 4.
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