Cook Johnson
01/19/2023 · Primary School
Divide. \[ \frac{-15 x^{5}+30 x^{4}-40}{5 x^{2}} \]
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To divide the expression
\[
\frac{-15 x^{5}+30 x^{4}-40}{5 x^{2}},
\]
we can separate the terms in the numerator and divide each by the denominator \(5 x^{2}\):
\[
\frac{-15 x^{5}}{5 x^{2}} + \frac{30 x^{4}}{5 x^{2}} - \frac{40}{5 x^{2}}.
\]
Now, we simplify each term:
1. For the first term:
\[
\frac{-15 x^{5}}{5 x^{2}} = -3 x^{3} \quad \text{(since } -15 \div 5 = -3 \text{ and } x^{5} \div x^{2} = x^{3}\text{)}
\]
2. For the second term:
\[
\frac{30 x^{4}}{5 x^{2}} = 6 x^{2} \quad \text{(since } 30 \div 5 = 6 \text{ and } x^{4} \div x^{2} = x^{2}\text{)}
\]
3. For the third term:
\[
\frac{-40}{5 x^{2}} = -\frac{8}{x^{2}} \quad \text{(since } -40 \div 5 = -8\text{)}
\]
Putting it all together, we have:
\[
-3 x^{3} + 6 x^{2} - \frac{8}{x^{2}}.
\]
Thus, the final result is:
\[
\boxed{-3 x^{3} + 6 x^{2} - \frac{8}{x^{2}}}.
\]
Quick Answer
\[
-3 x^{3} + 6 x^{2} - \frac{8}{x^{2}}.
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
(0)
Ask Real Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
PREV 
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
