Chapter 5 - Polynomials and Polynomial Functions - 5-2 Polynomials, Linear Factors, and Zeros - Practice and Problem-Solving Exercises - Page 293: 26

$f(x)=x^4+10x^3+35x^2+50x+24$

RECALL: If $a$ is a zero of a polynomial, then $x−a$ is a factor of the polynomial. Thus, having $x=-1, -2, -3, -4$ as zeros of the polynomial function means that $x+1,x+2, x+3$, and $x+4$ are factors of the polynomial. Therefore the function is $f(x)=(x+1)(x+2)(x+3)(x+4) \\f(x)=x^4+10x^3+35x^2+50x+24.$