Question
Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(-8 f^{2}-61 f+89\right) \div(f+9) \) Submit
Ask by Hardy Pearson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The division of \( -8f^{2} - 61f + 89 \) by \( f + 9 \) results in a quotient of \( -8f + 11 \) and a remainder of \( -10 \). Therefore, the final expression is:
\[
-8f + 11 - \frac{10}{f + 9}
\]
Solution
To divide the polynomial \( -8f^{2} - 61f + 89 \) by \( f + 9 \), follow these steps:
1. **Divide the leading terms:**
\[
\frac{-8f^2}{f} = -8f
\]
2. **Multiply the divisor by this result:**
\[
-8f \times (f + 9) = -8f^2 - 72f
\]
3. **Subtract this from the original polynomial:**
\[
(-8f^2 - 61f + 89) - (-8f^2 - 72f) = 11f + 89
\]
4. **Repeat the division with the new polynomial:**
\[
\frac{11f}{f} = 11
\]
5. **Multiply the divisor by this new result:**
\[
11 \times (f + 9) = 11f + 99
\]
6. **Subtract to find the remainder:**
\[
(11f + 89) - (11f + 99) = -10
\]
Putting it all together, the quotient is \( -8f + 11 \) with a remainder of \( -10 \). Therefore, the final answer is:
\[
-8f + 11 - \frac{10}{f + 9}
\]
**Answer:**
After simplifying, the division is –8 f + 11 minus ten over (f + 9). Thus,
−8f + 11 − 10⁄(f+9)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
Let's divide the polynomial \(-8f^2 - 61f + 89\) by \(f + 9\). 1. **Divide the leading term**: \(-8f^2 \div f = -8f\). 2. **Multiply**: \(-8f \cdot (f + 9) = -8f^2 - 72f\). 3. **Subtract**: \[ (-8f^2 - 61f + 89) - (-8f^2 - 72f) = 11f + 89. \] 4. **Repeat**: Divide the leading term \(11f \div f = 11\). 5. **Multiply**: \(11 \cdot (f + 9) = 11f + 99\). 6. **Subtract**: \[ (11f + 89) - (11f + 99) = -10. \] So, we get: \[ -8f - 11 - \frac{10}{f + 9}. \] The final answer is: \[ -8f - 11 - \frac{10}{f + 9}. \]
