Chapter 5 Polynomials and Polynomial Functions - 5.7 Apply the Fundamental Theorem of Algebra - 5.7 Exercises - Skill Practice - Page 384: 29

$x^4-x^3-18x^2+10x+8$

We need to write down the polynomial $f(x)$ in factored form. $f(x)=(x+4)(x-1)(x-2+\sqrt 6)(x-2-\sqrt 6)$ $=(x^2+3x-4)(x^2-4x+4-\sqrt{36})$ $=(x^2+3x-4)(x^2-4x-2)$ $=(x^2+3x-4) \times (x^2)-4x(x^2+3x-4)-2 \times (x^2+3x-4)$ $=x^4-4x^3-2x^2+3x^3-12x^2-6x-4x^2+16x+8$ $=x^4-x^3-18x^2+10x+8$