Answer :
By definition:
- The zeros of a function are also called roots and x-intercepts.
- The highest exponent of the variable of the function indicates the degree of the function.
In this case, knowing that the zeros of the function are:
[tex]\begin{gathered} x=-1 \\ x=1 \\ x=-5 \end{gathered}[/tex]You can write it in the following factored form:
[tex]f(x)=(x+1)(x-1)(x+5)[/tex]Simplifying it, you get:
[tex]\begin{gathered} f(x)=(x+1)(x-1)(x+5) \\ f(x)=(x^2-1)(x+5) \\ f(x)=(x^2)(x)+(x^2)(5)-(1)(x)-(1)(5) \\ f(x)=x^3+5x^2-x-5 \end{gathered}[/tex]Hence, the answer is: Option A.