Question

question
answer the questions about the following polynomial.
$-x^{3}+\frac{1}{6}$
answer attempt 1 out of 2
the expression represents a polynomial with \\(\square\\) terms. the constant term is \\(\square\\), the leading term is \\(\square\\), and the leading coefficient is \\(\square\\).

Explanation:

Step1: Determine the number of terms

A term in a polynomial is a single number or a product of a number and variables. In the polynomial \(-x^{3}+\frac{1}{6}\), we have two terms: \(-x^{3}\) and \(\frac{1}{6}\).

Step2: Identify the constant term

A constant term is a term without a variable. Here, the constant term is \(\frac{1}{6}\).

Step3: Identify the leading term

The leading term is the term with the highest degree. The degree of \(-x^{3}\) is 3 and the degree of \(\frac{1}{6}\) is 0. So the leading term is \(-x^{3}\).

Step4: Identify the leading coefficient

The leading coefficient is the coefficient of the leading term. For the leading term \(-x^{3}\), the coefficient is \(-1\). Also, the polynomial is a cubic (degree 3) polynomial since the highest degree is 3.

Answer:

The expression represents a cubic polynomial with 2 terms. The constant term is \(\frac{1}{6}\), the leading term is \(-x^{3}\), and the leading coefficient is \(-1\).