Chapter 5 Polynomials and Polynomial Functions - 5.7 Apply the Fundamental Theorem of Algebra - 5.7 Exercises - Skill Practice - Page 384: 27

$x^4-18x^3+122x^2-370x+425$

We need to write down the polynomial $f(x)$ in factored form. $f(x)=(x^2-10x+25)(x^2-8x+17)$ $=(x^2-10x+25)(x^2)-8x \times (x^2-10x+25)+17 \times ((x^2-10x+25)$ $=x^4-10x^3+25x^2-8x^3+80x^2-200x +17x^2-170x+425$ $=x^4+(10x^3-8x^3)+(25x^2+80x^2+17x^2)+(-200x -170x)+425$ $=x^4-18x^3+122x^2-370x+425$