is (x-2) a factor of f(x) = x^3 − 2x^2 + 2x + 3, use either remainder theorem or factor theorem to explain your reasoning

no

Step-by-step explanation:

divide the polynomials using polynomial division

       ___0    +  x^2    +   2

x - 2 |     x^3  -  2x^2  +  2x  +  3

           -  x^3  +  2x^2

                             0  +  2x  +  3

                                -  2x  +   4

                                             7

Since there is a remainder, (x-2) cannot be a factor of (x^3 - 2x^2 +2x + 3); because it does not divide evenly.