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Thread: Factor theorem

  1. #1
    Junior Member
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    Post Factor theorem

    Hi there, I have the math question that I have is giving me some problem.
    It said if $\displaystyle f(x)\equiv ax^2 + bx +c$ leaves remainders 1, 25, 1 on division by$\displaystyle x-1$, $\displaystyle x+1$, $\displaystyle x-2$ respectively, show that $\displaystyle f(x) $is a prfect square.
    can some one please help me with this problem?
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  2. #2
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    From your information

    $\displaystyle f(1) = 1$

    $\displaystyle a1^2 + b(1) +c = 1$

    $\displaystyle a+b+c = 1$ ...(1)



    $\displaystyle f(-1) = 25$

    $\displaystyle a(-1)^2 + b(-1) +c = 25$

    $\displaystyle a-b+c = 25$ ...(2)



    $\displaystyle f(2) = 1$

    $\displaystyle a(2)^2 + b(2) +c = 1$

    $\displaystyle 4a+2b+c = 1 $...(3)

    you now have 3 equations with 3 unknowns, find a,b, and c and try to factor the original equation as a perfect square.
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