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Determine rather the expression is a polynomial.

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A polynomial is a function that can be expressed in terms that only contain positive integer exponents and the operations of addition, subtraction, and multiplication (i.e., it is necessary that the expression can be written without division).

     5x2 - 3x - 5 

This is a polynomial since all its variables have positive integer exponents and does not require division. 

Each single number, variable, or numbers and variables being multiplied constitutes a term. With that, since 5 and x2 are being multiplied they make up a single term. Likewise, 3x is a another term as is 5. Therefore, this polynomial contains 3 terms. 

A variable is a symbol (usually an alphabetical letter like x, y, z, etc.) that represents an unknown number. Since we only see the variable x in this expression, there is only one variable.

The degree of a polynomial is the value of the greatest exponent in the terms of a polynomial. Here, the highest degree is found on the first term   5x2 , since the value of the exponent of this term is 2 the degree of the polynomial is 2.