Pregunta
What are the degree and leading coefficient of the polynomial? \( -7 w+6-w^{7}-8 w^{3} \) Degree: \( \square \) Leading coefficient:
Ask by Garrett Daniel. in the United States
Mar 09,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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Degree: 7
Leading coefficient: -1
Solución
1. Rewrite the polynomial in standard form (terms arranged in decreasing order of degree):
\[
-w^7 - 8w^3 - 7w + 6
\]
2. Identify the degree: The highest power of \( w \) is in the term \(-w^7\), so the degree is:
\[
7
\]
3. Determine the leading coefficient: The coefficient of the highest-degree term \(-w^7\) is:
\[
-1
\]
Degree: \( 7 \)
Leading coefficient: \( -1 \)
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Simplifique esta solución Extra Insights
The degree of the polynomial \( -7w + 6 - w^{7} - 8w^{3} \) is \( 7 \), which comes from the highest power of \( w \) found in the expression! That pesky \( -w^{7} \) takes the crown. Now, the leading coefficient is the coefficient of that term, which is \( -1 \) (as the term can be rewritten as \( -1 \cdot w^{7} \)). Game on for these polynomial properties!
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