Question

question
determine if the expression $b^4\sqrt{7}$ 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 a polynomial.

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 \(a_i\) are constants and \(n\) is a non - negative integer. The given expression is \(b^{4}\sqrt{7}=\sqrt{7}b^{4}\), which can be written in the form of a single term (a monomial, which is a type of polynomial) with coefficient \(\sqrt{7}\) (a constant) and the variable \(b\) raised to the power \(4\) (a non - negative integer).

Step2: Determine the type and degree

Since it has only one term, it is a monomial (a type of polynomial). The degree of a polynomial in one variable is the highest power of the variable. For the polynomial \(\sqrt{7}b^{4}\), the power of \(b\) is \(4\), so the degree is \(4\).

Answer:

The given expression \(\boldsymbol{\text{is}}\) a polynomial. It is a monomial (a type of polynomial) with degree \(4\).