Question

question
determine if the expression $-sqrt{5}$ is a polynomial or not. if it is a polynomial, state the type and
degree of the polynomial.

answer attempt 1 out of 2
the given expression represents a polynomial. the polynomial is a
and has a degree of

Explanation:

Step1: Recall Polynomial Definition

A polynomial is an expression of the form \(a_nx^n + a_{n - 1}x^{n - 1}+\dots+a_1x + a_0\), where \(n\) is a non - negative integer and \(a_i\) are constants. A constant term (a term without a variable) is a polynomial of degree 0, also called a constant polynomial or a monomial (since it has one term). The expression \(-\sqrt{5}\) can be written as \(0x^n+\dots+0x+(-\sqrt{5})\) for any non - negative integer \(n\). In the standard form of a polynomial, when we consider the term with \(x^0\) (since \(x^0 = 1\)), we have \(-\sqrt{5}x^0\).

Step2: Determine the Type and Degree

Since \(-\sqrt{5}\) has only one term, it is a monomial (a type of polynomial with one term). For a polynomial of the form \(ax^k\), the degree is the highest power of \(x\) with a non - zero coefficient. In the case of \(-\sqrt{5}=-\sqrt{5}x^0\), the power of \(x\) is \(0\), so the degree of the polynomial is \(0\).

Answer:

The given expression represents a polynomial. The polynomial is a monomial and has a degree of \(0\).