Option: D is the correct answer.
D. The product p(x) and q(x) is a polynomial .
We are given two polynomials p(x) and q(x) as follows:
[tex]p(x)=a_0+a_1x+a_2x^2+....+a_nx^n[/tex]
[tex]q(x)=b_0+b_1x+b_2x^2+......+b_mx^m[/tex]
Now we do not know the degree of p(x) and q(x) i.e. we do not know the value of m and n respectively and also the coefficients.
Hence, we can't say that the product of these two polynomials is a real number, binomial (i.e. polynomial of degree 2) or a integer.
But we know that the product of two polynomial is always a polynomial may be a constant polynomial , zero polynomial or a polynomial of degree n.
Hence, the product of p(x) and q(x) is a polynomial.