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Math Help - Polynomial help

  1. #1
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    Polynomial help

    The polynomial P(x) has remainder 1 when divided by (x-1) , and remainder 3 when divided by (x+1) . Find the remainder when P(x) is divided by (x^2-1).
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  2. #2
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    Quote Originally Posted by mathaddict View Post
    The polynomial P(x) has remainder 1 when divided by (x-1) , and remainder 3 when divided by (x+1) . Find the remainder when P(x) is divided by (x^2-1).
    P(x) = Q(x) (x - 1)(x + 1) + (ax + b) where Q(x) is a polynomial.

    When P(x) is divided by (x^2-1) the remainder is ax + b.

    Now note:

    P(1) = 1 => 1 = a + b .... (1)

    P(-1) = 3 => 3 = -a + b .... (2)

    Solve equations (1) and (2) simultaneously.
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