Final answer:
The expression -7c^3d is a polynomial, specifically a monomial, and its degree is 4.
Step-by-step explanation:
The expression -7c^3d is indeed a polynomial. A polynomial is an algebraic expression consisting of variables, also called indeterminates, raised to non-negative integer powers, and multiplied by coefficients. They can have one or several terms. In this case, the given expression has a single term, which is known as a monomial.
The degree of a polynomial is determined by the highest sum of the exponents of the variables in any single term. In the expression -7c^3d, c is raised to the 3rd power and d to the 1st power. Adding these exponents together, we get a total degree of 4 for the polynomial. Therefore, it is a 4th degree monomial.
To verify that an expression is a polynomial and to determine its degree, you should:
Ensure all exponents of variables are non-negative integers.
Add up the exponents to find the degree.
Check the answer to see if it is reasonable.