If $\displaystyle f(x)=ax^2+bx+c$ 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 ?
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 $\displaystyle ax^2+bx+c$ is a perfect square, then $\displaystyle ax^2+bx+c = (kx+d)^2$