Question

zeros: -1, 0, 7 ; degree 3

Answer 1

I take it you want a third degree polynomial function f(x) that has zeros at those given x values?

Answer 2

If so, this is an easy enough problem!

Lets start by assuming the coefficient on the largest degree is 1.

Now lets write what you want in factored form

since you want a zero at -1, 0 and 7, you know that when x is any of these values the function is zero.
Lets solve for the constant values for each of these cases:
if x+b=0 and x=-1,
then -1+b=0
b=1
x=0, 0+b=0, b=0
x=7, 7+b=0, b=-7

We can translate that into (x+1)*(x)*(x-7)=f(x)

Notice that if you put any of the zero x values in, your function will be zero, because zero times any number has to be zero!

Now it just depends what the question is asking for. Technically, this is your function, but questions like this generally ask for you to expand your function first. So just multiply these terms together and your done!