Chapter 5 - Polynomials and Polynomial Functions - 5-2 Polynomials, Linear Factors, and Zeros - Practice and Problem-Solving Exercises - Page 293: 24

$f(x)=x^3-\frac{7}{2}x^2-2x$

RECALL: If $a$ is a zero of a polynomial, then $x−a$ is a factor of the polynomial. Thus, having $x=0, 4, -\frac{1}{2}$ as zeros of the polynomial function means that $x,x-4$, and $x+\frac{1}{2}$ are factors of the polynomial. Therefore the function is $f(x)=x(x-4)(x+\frac{1}{2}) \\f(x)=x^3-\frac{7}{2}x^2-2x.$