Question

expressions-polynomials-evaluate add subtract poly
(1 point)
determine the following for: (-2x^8)
a) determine the coefficient and the degree of each term.

term	coefficient	degree
(0x^7)	(square)	(square)

b) the degree of the polynomial is (square),
the leading term is (square),
and the leading coefficient is (square).
note:

Explanation:

Part a)

For the term \(-2x^8\):

Step1: Find the coefficient

The coefficient of a term is the numerical factor. For \(-2x^8\), the numerical factor is \(-2\), so the coefficient is \(-2\).

Step2: Find the degree

The degree of a term with a single variable \(x\) is the exponent of \(x\). For \(-2x^8\), the exponent of \(x\) is \(8\), so the degree is \(8\).

For the term \(0x^7\):

Step1: Find the coefficient

The numerical factor here is \(0\), so the coefficient is \(0\).

Step2: Find the degree

The exponent of \(x\) is \(7\), but since the coefficient is \(0\), the term is essentially \(0\). However, following the definition, the degree of \(0x^7\) (as a term) is \(7\) (but note that a term with coefficient \(0\) doesn't contribute to the polynomial's degree).

Part b)

Step1: Degree of the polynomial

The degree of a polynomial is the highest degree of its non - zero terms. The non - zero term here is \(-2x^8\) with degree \(8\), so the degree of the polynomial is \(8\).

Step2: Leading term

The leading term of a polynomial is the term with the highest degree. Here, the term with the highest degree is \(-2x^8\), so the leading term is \(-2x^8\).

Step3: Leading coefficient

The leading coefficient is the coefficient of the leading term. For the leading term \(-2x^8\), the coefficient is \(-2\), so the leading coefficient is \(-2\).

Filling the table for part a)

Term	Coefficient	Degree
\(0x^7\)	\(0\)	\(7\)

Answer:

s for part b)

• The degree of the polynomial is \(\boldsymbol{8}\)
• The leading term is \(\boldsymbol{-2x^8}\)
• The leading coefficient is \(\boldsymbol{-2}\)

Final Answers (for the table and part b)

Part a) Table:

• For \(-2x^8\): Coefficient = \(-2\), Degree = \(8\)
• For \(0x^7\): Coefficient = \(0\), Degree = \(7\)

Part b)

• Degree of polynomial: \(8\)
• Leading term: \(-2x^8\)
• Leading coefficient: \(-2\)