Question

answer the questions about the following polynomial.
$-3x^4 - 1$
answer attempt 1 out of 9
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 \(-3x^4 - 1\), the terms are \(-3x^4\) and \(-1\), so there are 2 terms.

Step2: Identify the constant term

A constant term is a term without a variable. Here, the constant term is \(-1\).

Step3: Find the leading term

The leading term is the term with the highest degree. The degree of \(-3x^4\) is 4 and the degree of \(-1\) (which can be thought of as \(-1x^0\)) is 0. So the leading term is \(-3x^4\).

Step4: Determine the leading coefficient

The leading coefficient is the coefficient of the leading term. For the leading term \(-3x^4\), the coefficient is \(-3\). Also, the polynomial is a quartic (degree 4) polynomial since the highest degree is 4.

Answer:

The expression represents a quartic (or 4th - degree) polynomial with 2 terms. The constant term is \(-1\), the leading term is \(-3x^4\), and the leading coefficient is \(-3\).