Question
Find the quotient of \( -8 s^{5}-2 s^{4}-14 s^{3}+4 s^{2} \) divided by \( 2 s^{2} \)
Ask by Wyatt Simmons. in the United States
Feb 05,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The quotient is \( -4s^{3} - s^{2} - 7s + 2 \).
Solution
To find the quotient of \( -8 s^{5} - 2 s^{4} - 14 s^{3} + 4 s^{2} \) divided by \( 2 s^{2} \), you can divide each term of the polynomial by \( 2 s^{2} \) individually.
\[
\begin{align*}
\frac{-8 s^{5}}{2 s^{2}} &= -4 s^{3} \\
\frac{-2 s^{4}}{2 s^{2}} &= -s^{2} \\
\frac{-14 s^{3}}{2 s^{2}} &= -7 s \\
\frac{4 s^{2}}{2 s^{2}} &= 2 \\
\end{align*}
\]
Combining these results, the quotient is:
\[
-4 s^{3} - s^{2} - 7 s + 2
\]
**Final Answer:**
\[
-4\,s^{3}\;-\;s^{2}\;-\;7\,s\;+\,2
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the quotient of \( -8 s^{5}-2 s^{4}-14 s^{3}+4 s^{2} \) divided by \( 2 s^{2} \), we can divide each term in the polynomial by \( 2 s^{2} \). 1. \( \frac{-8 s^{5}}{2 s^{2}} = -4 s^{3} \) 2. \( \frac{-2 s^{4}}{2 s^{2}} = -s^{2} \) 3. \( \frac{-14 s^{3}}{2 s^{2}} = -7 s \) 4. \( \frac{4 s^{2}}{2 s^{2}} = 2 \) Now, we combine all the results: The quotient is: \[ -4 s^{3} - s^{2} - 7 s + 2 \]
