What is meant by the degree of a polynomial?

• A. The number of terms in the polynomial
• B. The highest power of the variable in the polynomial expression
• C. The total sum of coefficients in the polynomial
• D. The product of all coefficients

Answer: (B)

The degree of a polynomial refers to the highest power of the variable that appears in the polynomial expression. For instance, in the polynomial (3x^4 + 2x^3 - x + 5), the highest exponent of the variable (x) is 4, which means this polynomial is of degree 4. The degree provides important information about the behavior of the polynomial, such as the number of roots it may have and the end behavior of its graph.

In contrast, other characteristics like the number of terms, the total sum of coefficients, or the product of coefficients do not define the polynomial's degree. The degree is solely determined by the term with the largest exponent of the variable.