Answer
$f(x)=x^3-6x^2+7x+2$
Work Step by Step
$f(x)=a(x-2)[x-(2+\sqrt 5)][x-(2-\sqrt 5)]=a(x-2)[(x-2)-\sqrt 5][(x-2)+\sqrt 5]=a(x-2)[(x-2)^2-(\sqrt 5)^2]=a(x-2)(x^2-4x+4-5)=a(x-2)(x^2-4x-1)=a(x^3-6x^2+7x+2)$
$a$ can be any value. If $a=1$:
$f(x)=x^3-6x^2+7x+2$
