Chapter 5 Polynomials and Polynomial Functions - Standardized Test Practice - Multiple Choice - Page 411: 13

Answer A

Using the Factor Theorem, if $x=a$ is a factor, then $(x-a)$ is a factor of $f(x)$. Hence here $f(x)=(x-(-1))(x-3)(x-(-4I))(x-4I)\\=(x+1)(x+4i)(x-4i)(x-3)\\=(x^2-6x+3)(x-1)(x+2i)(x-2i)\\=(x+4i)(x-4i)(x^2-2x-3)\\=(x^2+16)(x^2-2x-3)\\=x^4-2x^3+13x^2-32x-48$ Hence, the correct answer is $A$.