Fill in the blank(s) to correctly complete each sentence. A polynomial function with leading term 3x⁵ has degree ____.

Verified step by step guidance

1. Recall that the degree of a polynomial function is the highest power of the variable in the polynomial.
2. Identify the leading term of the polynomial, which is the term with the highest exponent on the variable.
3. In this problem, the leading term is given as \$3x^{5}\(, where the exponent on \)x$ is 5.
4. Therefore, the degree of the polynomial function is the exponent of the leading term, which is 5.
5. Fill in the blank with the number 5 to complete the sentence: "A polynomial function with leading term \$3x^{5}$ has degree 5."

Key Concepts

Polynomial Function

A polynomial function is an expression consisting of variables and coefficients combined using only addition, subtraction, multiplication, and non-negative integer exponents. For example, 3x^5 + 2x^3 - 7 is a polynomial function.

Leading Term

The leading term of a polynomial is the term with the highest power of the variable, which determines the polynomial's end behavior. In 3x^5 + 2x^3, the leading term is 3x^5.

Degree of a Polynomial

The degree of a polynomial is the highest exponent of the variable in the polynomial. It indicates the polynomial's overall degree and influences its graph's shape. For example, the degree of 3x^5 is 5.