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: 5

$f(x)=x^4-16x^3+61x^2+114x-720$

Using the Factor Theorem, if $x=a$ is a factor, then $(x-a)$ is a factor of $f(x)$. Hence here $f(x)=(x-(-3))(x-5)(x-(7+\sqrt 2))(x-(7-\sqrt 2))\\=(x+3)(x-5)(x-7-\sqrt 2)(x-7+\sqrt 2)\\=(x^2-14x+47)(x-5)(x+3)\\=(x^2-2x-15)(x^2-14x+48)\\=x^4-16x^3+61x^2+114x-720\\=x^4-16x^3+61x^2+114x-720$