Question

what are the leading coefficient and degree of the polynomial?
-7w² - 2 + w⁷ - 20w
leading coefficient:
degree:

Explanation:

Step1: Rearrange the polynomial

First, we rearrange the polynomial in descending order of the exponents of \( w \). The given polynomial is \( -7w^{2}-2 + w^{7}-20w \). Rearranging it, we get \( w^{7}-7w^{2}-20w - 2 \).

Step2: Find the leading coefficient

The leading term of a polynomial (when arranged in descending order of exponents) is the term with the highest degree. Here, the leading term is \( w^{7} \), which can be written as \( 1\times w^{7} \). So, the leading coefficient is the coefficient of the leading term, which is \( 1 \).

Step3: Find the degree of the polynomial

The degree of a polynomial is the highest power (exponent) of the variable in the polynomial. In the rearranged polynomial \( w^{7}-7w^{2}-20w - 2 \), the highest exponent of \( w \) is \( 7 \). So, the degree of the polynomial is \( 7 \).

Answer:

Leading coefficient: \( 1 \)
Degree: \( 7 \)