The Value of r(2) is -6 and x-2 is not a factor of r(x).
What is the value of a function on a Variable?
A real-valued function of a real variable is a function that takes as input a real number, commonly represented by the variable x, for producing another real number, the value of the function, commonly denoted f(x).
What is Factor?
A factor of polynomial P(x) is any polynomial that divides evenly into P(x).
How to find out the value of r(x)?
Given r(x)=x^3-4x^2+4x-6,
Put x = 2 ,
r(2)=2^3-4(2)^2+4(2)-6
r(2)=8-16+8-6
r(2)=-6
As we see that x=2 is not equal to zero,
implies x-2 does not divide r(x) evenly.
thus x-2 is not a factor of given r(x).