Question

answer the questions about the following polynomial. $7x^3 - \frac{1}{6} + x^2$ 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: Identify the number of terms

A term is a single number or a product of a number and variables. The polynomial \(7x^3 - \frac{1}{6}+x^2\) can be rewritten as \(7x^3 + x^2-\frac{1}{6}\). The terms are \(7x^3\), \(x^2\), and \(-\frac{1}{6}\), so there are 3 terms.

Step2: Determine the type of polynomial (degree)

The degree of a polynomial is the highest power of \(x\) in the polynomial. The powers of \(x\) here are 3 (in \(7x^3\)), 2 (in \(x^2\)), and 0 (in the constant term \(-\frac{1}{6}\)). The highest power is 3, so it's a cubic polynomial.

Step3: Find the constant term

The constant term is the term without a variable, which is \(-\frac{1}{6}\).

Step4: Identify the leading term

The leading term is the term with the highest degree (highest power of \(x\)). The term with degree 3 is \(7x^3\), so that's the leading term.

Step5: Find the leading coefficient

The leading coefficient is the coefficient of the leading term. For \(7x^3\), the coefficient is 7.

Answer:

The expression represents a cubic polynomial with 3 terms. The constant term is \(-\frac{1}{6}\), the leading term is \(7x^3\), and the leading coefficient is 7.