Question

If a polynomial p(x) is divisible by (x-2) and 4 is a zero of p(x), write a factor of p(x) of degree 2.

Answer 1

If p(x) is divisible by (x-2), then (x-2) is a factor. If 4 is a zero of p(x), then (x-4) is a factor. The product of these two different factors is also a factor of p(x). The degree 2 factor you want is ...
  (x-2)(x-4) = x² -6x +8