Question

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

f(x) = x4 + 4x3 + 6x2 + 4x + 5; d(x) = x2 + 1

A. f(x) = (x2 + 1)( x2 + 4x + 5) + 12x - 15
B. f(x) = (x2 + 1)( x2 + 4x + 5)
C. f(x) = (x2 + 1)( x2 - 4x + 5)
D. f(x) = (x2 + 1)( x2 - 4x + 5) + 12x - 15

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.`