Question

answer the questions about the following polynomial.

$-10x^4 - 7$

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 \(-10x^4 - 7\), we can separate the terms as \(-10x^4\) and \(-7\). So there are 2 terms.

Step2: Identify the constant term

A constant term is a term without a variable. In the polynomial, the term \(-7\) has no variable, so the constant term is \(-7\).

Step3: Find the leading term

The leading term is the term with the highest degree. The degree of a term is the sum of the exponents of its variables. For \(-10x^4\), the degree is 4, and for \(-7\) (which can be thought of as \(-7x^0\)), the degree is 0. So the leading term is \(-10x^4\).

Step4: Determine the leading coefficient

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

Step5: Determine the type of polynomial (degree)

The degree of the polynomial is the degree of the leading term, which is 4. So it's a quartic (or 4th - degree) 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 \(\boldsymbol{-10}\).