Find a polynomial function P(x) with the given zeros. There is no unique answer for 1,0,-1 p(x)=
It would help if you proofread your questions before you posted them.
What "given zeros"?
p(x) = (x-1)(x-0)(x+1) = x(x^2-1) = ___
Extra credit: why is this not unique?
To find a polynomial function with the given zeros, we can make use of the fact that if a number a is a zero of a polynomial function P(x), then (x - a) is a factor of P(x).
Since the zeros are 1, 0, and -1, we can write the polynomial function as:
P(x) = a(x - 1)(x - 0)(x + 1)
To find the value of 'a', we need additional information. If you provide any other point on the graph of P(x) or the degree of the polynomial function, we can determine the exact polynomial function.