Answer the following questions based on the idea of zeros and factors of a polynomial.
(i) Define a zero of a polynomial.
(ii) Prove that if x=a is a zero of a polynomial p(x), then (x−a) is a factor of p(x).
(iii) Give an example of a cubic polynomial with integer coefficients, identify one of its zeros, and verify explicitly that the corresponding linear expression divides the polynomial exactly.