Chapter 5 Polynomials and Polynomial Functions - 5.7 Apply the Fundamental Theorem of Algebra - 5.7 Exercises - Skill Practice - Page 384: 25

$x^4-4x^3+14x^2-36x+45$

We need to write down the polynomial $f(x)$ in factored form. $f(x)=(x-3i)(x+3i)[x-(2-i)][x-(2+i)]=(x^2+9)[(x-2)^2+1]$ $=(x^2+9)[x^2-4x+5)$ $=x^4-4x^3+5x^2+9x^2-36x+45$ $=x^4-4x^3+14x^2-36x+45$