To analyze the given polynomial, we need to identify its degree, count the number of terms, and determine specific characteristics such as the constant term, leading term, and leading coefficient. The degree of the polynomial is determined by the highest power of \( x \). The constant term is the term without \( x \). The leading term is the term with the highest power of \( x \), and the leading coefficient is the coefficient of the leading term.
The degree of a polynomial is the highest power of \( x \) present in the expression. In the polynomial \(-\frac{x^5}{5} + 4x^3 + x^2 - 3x - 1\), the highest power of \( x \) is 5. Therefore, the degree of the polynomial is \( 5 \).
The polynomial \(-\frac{x^5}{5} + 4x^3 + x^2 - 3x - 1\) consists of five distinct terms: \(-\frac{x^5}{5}\), \(4x^3\), \(x^2\), \(-3x\), and \(-1\). Thus, the number of terms is \( 5 \).
The constant term in a polynomial is the term without any \( x \) variable. In this polynomial, the constant term is \(-1\).
The leading term of a polynomial is the term with the highest power of \( x \). Here, the leading term is \(-\frac{x^5}{5}\). The leading coefficient is the coefficient of the leading term, which is \(-\frac{1}{5}\).
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