Question

answer the following questions using what youve learned from this lesson. write your responses in the space provided. 1. which of the following are monomials? select all that apply. hint: a monomial has one term and is usually in the form $ax^n$, where $n$ is a nonnegative integer. a constant is also a monomial. a. $-4x^2$ b. $x^2 - 4$ c. $\frac{4}{x}$ d. 14 e. $4x^{-2}$

Explanation:

Step1: Analyze Option A

A monomial is in the form \(ax^n\) with \(n\) a non - negative integer. For \(-4x^{2}\), \(a = - 4\) and \(n=2\) (a non - negative integer), so it is a monomial.

Step2: Analyze Option B

\(x^{2}-4\) has two terms (\(x^{2}\) and \(-4\)), so it is a binomial, not a monomial.

Step3: Analyze Option C

\(\frac{4}{x}=4x^{-1}\), here \(n=-1\) which is negative, so it does not fit the form of a monomial (\(n\) should be non - negative). So it is not a monomial.

Step4: Analyze Option D

A constant is a monomial. 14 is a constant, so it is a monomial.

Step5: Analyze Option E

\(4x^{-2}\) has \(n = - 2\) (negative), so it does not fit the form of a monomial (\(n\) should be non - negative). So it is not a monomial.

Answer:

A. \(-4x^{2}\), D. 14