Chapter 5 Polynomials and Polynomial Functions - 5.7 Apply the Fundamental Theorem of Algebra - 5.7 Exercises - Skill Practice - Page 384: 32

$x^3-4x^2+6x-4$

We need to write down the polynomial $f(x)$ in factored form. $f(x)=(x-2)[x-(1+i)][x-(1-i)]$ $=(x-2)(x-1-i)(x-1+i)$ $=(x-2)(x^2-x+xi-x+1-i-xi+i-i^2)$ $=(x-2)(x^2-2x+2)$\ $=x^3-2x^2+2x-2x^2+4x-4$ $=x^3-4x^2+6x-4$