Explanation:

Polynomial is a mathematical expression that contains variables, constants and exponents, combined using arithmetic operations like addition, subtraction, multiplication and division.

Degree of a polynomial is the highest power of the variable in the polynomial.

For example, in the polynomial 2x^3 + 5x^2 - 7x + 4, the degree is 3.

A polynomial of degree 5 in x means that the highest power of x in the polynomial is 5.

Now, let's consider the number of terms in a polynomial of degree 5 in x.

A term in a polynomial is a product of a constant and one or more variables raised to some exponents.

For example, in the polynomial 2x^3 + 5x^2 - 7x + 4, the terms are 2x^3, 5x^2, -7x and 4.

The number of terms in a polynomial of degree 5 in x depends on the number of possible combinations of the variables and constants that can be multiplied together to obtain a term of degree 5.

To obtain a term of degree 5 in x, we can multiply x^5 by a constant, or we can multiply x^4 by x and a constant, or we can multiply x^3 by x^2 and a constant, and so on.

Thus, the number of possible terms in a polynomial of degree 5 in x is given by the sum of the binomial coefficients of the form (5 choose k), where k ranges from 0 to 5.

(5 choose 0) + (5 choose 1) + (5 choose 2) + (5 choose 3) + (5 choose 4) + (5 choose 5) = 1 + 5 + 10 + 10 + 5 + 1 = 32

Therefore, a polynomial of degree 5 in x can have at most 32 terms.

However, not all of these terms need to be present in the polynomial. Some of the terms may have a coefficient of 0, which means that they do not contribute to the polynomial.

For example, the polynomial x^5 + 2x^3 - x^2 - 3x + 4 has 5 terms, even though it is of degree 5 in x.

Thus, the correct answer is option 'C', which states that a polynomial of degree 5 in x has at most 6 terms.