Question 1042147
{{{f(x)=a(x+4)(x-(1+2i))(x-(1-2i))}}}, a is unknown factor, determinable later using x=2.


{{{f(x)=a(x+4)(x-1-2i)(x-1+2i)}}}
{{{f(x)=a(x+4)((x-1)-2i)((x-1)+2i)}}}
{{{a(x+4)(x^2-2x+1-4(-1))}}}
{{{highlight(f(x)=a(x+4)(x^2-2x+5))}}}


FINDING FACTOR a
{{{f(2)=30}}} as given
{{{a(2+4)(2^2-2*2+5)=30}}}
{{{a*6*5=30}}}
{{{a=1}}}


THE FUNCTION f
{{{highlight(f(x)=(x+4)(x^2-2x+5))}}}
Do the multiplication to put into general polynomial form.