Chapter 5 - Polynomials and Polynomial Functions - 5-2 Polynomials, Linear Factors, and Zeros - Practice and Problem-Solving Exercises - Page 293: 19

$f(x)=x^3-18x^2+107x-210$

RECALL: If $a$ is a zero of a polynomial, then $x-a$ is a factor of the polynomial. Thus, having x=5, 6, 7 as zeros of the polynomial function means that $x-5, x-6$, and $x-7$ are factors of the polynomial. Therefore the function is $f(x)=(x-5)(x-6)(x-7) \\f(x)=x^3-18x^2+107x-210.$