Question
Find the degree and leading coefficient of the polynomial \( 9 y+7 y^{3}-5-4 y^{2} \). Select the correct answer below: Degree: 1 . Leading coefficient: 9 . Degree: 9 . Leading coefficient: 1 . Degree: 3 . Leading coefficient: 7 . Degree: 7 . Leading coefficient: 3 . Degree 2 . Leading coefficient: -4 .
Ask by Olson Ayala. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The degree of the polynomial is 3 and the leading coefficient is 7.
Solution
1. Write the polynomial in descending order of degree:
\[
7y^3 - 4y^2 + 9y - 5
\]
2. Identify the highest power of \( y \). The term \( 7y^3 \) shows that the polynomial is of degree \( 3 \).
3. The leading coefficient is the coefficient of the highest degree term, which is \( 7 \).
Thus, the degree of the polynomial is \( 3 \) and the leading coefficient is \( 7 \).
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Simplify this solution Mind Expander
To find the degree and leading coefficient of the polynomial \( 9y + 7y^3 - 5 - 4y^2 \), we first rearrange the terms in descending order based on their powers of \( y \): \( 7y^3 - 4y^2 + 9y - 5 \). The highest power is \( 3 \), so the degree of the polynomial is \( 3 \). The leading coefficient, which is the coefficient of the term with the highest degree, is \( 7 \). So, the correct answer is: Degree: 3 . Leading coefficient: 7 .
