Chapter 5 - Polynomials and Polynomial Functions - 5-2 Polynomials, Linear Factors, and Zeros - Practice and Problem-Solving Exercises - Page 293: 25

$f(x)=x^4-5x^3+6x^2$

RECALL: If $a$ is a zero of a polynomial, then $x−a$ is a factor of the polynomial. Thus, having $x=0, 0, 2, 3$ as zeros of the polynomial function means that $x,x, x-2$, and $x-3$ are factors of the polynomial. Therefore the function is $f(x)=x(x)(x-2)(x-3) \\f(x)=x^4-5x^3+6x^2.$