Divide. If the polynomial does not divide evenly, include the remainder as a fraction.

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Jan 23,2025

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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

UpStudy AI · Accepted Answer

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)
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: $$ -8f + 11 - \frac{10}{f + 9} $$

Divide. If the polynomial does not divide evenly, include the remainder as a fraction.

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Divide. If the polynomial does not divide evenly, include the remainder as a fraction. Submit