Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i
and 2-2i
review andrew's work, identify the error and correct all work from that point forward that is affected by this
error. include at least one sentence explaining his error

Error of Andrew: Made incorrect factors from the roots

Step-by-step explanation:

Roots of the polynomial are: 3, 2 + 2i, 2 - 2i. According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is  a factor of P(x). According to this definition:

(x - 3) , (x - (2 + 2i)) , (x - (2 - 2i)) are factors of the required polynomial.

Simplifying the brackets, we get:

(x - 3), (x - 2 - 2i), (x - 2 + 2i) are factors of the required polynomial.

This is the step where Andrew made the error. The factors will always be of the form (x - a) , not (x + a). Andrew wrote the complex factors in form of (x + a)  which resulted in the wrong answer.

So, the polynomial would be: