Chapter 5 Polynomials and Polynomial Functions - 5.9 Write Polynomial Functions and Models - 5.9 Exercises - Quiz for Lessons 5.7-5.9 - Page 399: 4

$f(x)=x^3-6x^2+10x-8$

Using the Factor Theorem, if $x=a$ is a factor, then $(x-a)$ is a factor of $f(x)$. Hence here $f(x)=(x-4)(x(1+i))(x-(1-i))\\=(x-4)(x-1-i)(x-1+i)\\=(x^2-2x+2)(x-4)\\=x^3-4x^2-2x^2+8x+2x-8\\=x^3-6x^2+10x-8$