Question

question
answer the questions about the following polynomial.
$6x^{3} + \frac{1}{10}$
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 is a single number or a product of a number and variables. In the polynomial \(6x^{3}+\frac{1}{10}\), we have two terms: \(6x^{3}\) and \(\frac{1}{10}\).

Step2: Identify the constant term

A constant term is a term without a variable. Here, the constant term is \(\frac{1}{10}\) since it has no \(x\) associated with it.

Step3: Identify the leading term

The leading term is the term with the highest degree. The degree of a term is the exponent of the variable. For \(6x^{3}\), the degree is 3, and for \(\frac{1}{10}\), the degree is 0. So the leading term is \(6x^{3}\).

Step4: Identify the leading coefficient

The leading coefficient is the coefficient of the leading term. The leading term is \(6x^{3}\), so the leading coefficient is 6.

Step5: Determine the type of polynomial (degree)

The degree of the polynomial is the degree of the leading term, which is 3. So it is a cubic polynomial (since degree 3 is cubic).

Answer:

The expression represents a cubic polynomial with 2 terms. The constant term is \(\frac{1}{10}\), the leading term is \(6x^{3}\), and the leading coefficient is 6.