Question 1113728
Another root is  {{{highlight(2-i)}}}, so part of the factorization for p is  {{{(x-(2+i))(x-(2-i))}}}
{{{(x-2-i)(x-2+i)}}}
{{{((x-2)-i)((x-2)+i)}}}
{{{(x-2)^2+1}}}
{{{x^2-4x+4+1}}}
{{{x^2-4x+5}}}--------a quadratic factor of p.


If you perform polynomial division for p(x) divided by {{{x^2-4x+5}}}, the result will be quotient of {{{x^2-2}}}.  The roots corresponding to this are  {{{highlight(-sqrt(2))}}} and {{{highlight(sqrt(2))}}}.