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Math Help - Remainder And Factor Theorem Question

  1. #1
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    Remainder And Factor Theorem Question

    Hi Guys,

    Got stuck with this polynomial question needing help !

    The question is as follows :

    When a polynomial h(x) is divided by (x-1) and (x+3) , the remainders are -2 and 10 respectively. Find the remainder when h(x) is divided by (x-1)(x+3)

    Please help guys !

    so vexed over this question !

    Thanks !
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  2. #2
    MHF Contributor
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    Suppose h(x) = (x - 1)(x + 3)f(x) + (ax + b) for some polynomial f(x) and two numbers a and b (the remainder must have the degree at most 1). We know that h(1) = -2 and h(-3) = 10. This gives two equations on a and b.
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  3. #3
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    hi sorry but i dont understand why h(x) = (x - 1)(x + 3)f(x) + (ax + b)
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  4. #4
    Senior Member BAdhi's Avatar
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    degree reduces

    if you divide a polynomial with a n degree polynomial, the remainder will be a n-1degree polynomial
    Last edited by BAdhi; December 10th 2010 at 07:15 AM. Reason: wrong example
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