# Math Help - Factor theorem

1. ## Factor theorem

Hi there, I have the math question that I have is giving me some problem.
It said if $f(x)\equiv ax^2 + bx +c$ leaves remainders 1, 25, 1 on division by $x-1$, $x+1$, $x-2$ respectively, show that $f(x)$is a prfect square.

$f(1) = 1$

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

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

$f(-1) = 25$

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

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

$f(2) = 1$

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

$4a+2b+c = 1$...(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.