Question

answer the questions about the following polynomial.
$-10x^4 - 7$
answer attempt 1 out of 2
the expression represents a
polynomial with
terms. the constant term is
, the leading term is
, and the leading coefficient is
.

Explanation:

Step1: Determine the number of terms

A polynomial term is a single number or a product of a number and variables. In \(-10x^4 - 7\), we have two terms: \(-10x^4\) and \(-7\).

Step2: Identify the constant term

A constant term has no variables. Here, the constant term is \(-7\).

Step3: Find the leading term

The leading term is the term with the highest degree. The degree of \(-10x^4\) is \(4\) and the degree of \(-7\) (which can be written as \(-7x^0\)) is \(0\). So the leading term is \(-10x^4\).

Step4: Determine the leading coefficient

The leading coefficient is the coefficient of the leading term. For \(-10x^4\), the coefficient is \(-10\).

Step5: Classify the polynomial by degree

The highest degree of the polynomial is \(4\), so it is a quartic (or 4th - degree) polynomial. Also, since there are two terms, it is a binomial. But the first blank is about the type (degree - related). The degree is 4, so it's a quartic polynomial.

Answer:

The expression represents a \(\boldsymbol{\text{quartic (4th - degree)}}\) polynomial with \(\boldsymbol{2}\) terms. The constant term is \(\boldsymbol{-7}\), the leading term is \(\boldsymbol{-10x^4}\), and the leading coefficient is \(\boldsymbol{-10}\).