Question

Divide f(x) by d(x), and write a summary statement in the form indicated.

Answer 1

Hello,
Answer B.

x²+1=(x-i)(x+i)

$x^4+4x^3+x^2+4x+5=(x-i)(x^3+(4+i)x^2+(5+4i)x+5i)\\ =(x-i)(x+i)(x^2+4x+5)=(x^2+1)(x^2+4x+5) \\ by\ synthetic\ division.$