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Math Help - remainder theorem

  1. #1
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    remainder theorem

    If f(x)=ax^2+bx+c has remainder 1 ,25 , and 1 when divided by ( x-1) , ( x+1 ), and (x-2) respcetively , show that the function f(x) is a perfect square .

    What does it mean when the function is a perfect square ?
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  2. #2
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    if f has remainder 1 when divided by (x-1), then f(1) = 1

    if f has remainder 25 when divided by (x+1), then f(-1) = 25

    if f has remainder 1 when divided by (x-2), then f(2) = 1

    a + b + c = 1

    a - b + c = 25

    4a + 2b + c = 1

    solve for a, b, and c

    if ax^2+bx+c is a perfect square, then ax^2+bx+c = (kx+d)^2
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