Question
Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( (-45 x-74) \div(5 x+9) \) Submithy
Ask by Gross Little. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The division of \(-45x - 74\) by \(5x + 9\) results in \(-9\) with a remainder of \(\frac{7}{5x + 9}\).
Solution
To divide the polynomial \(-45x - 74\) by \(5x + 9\), follow these steps:
1. **Divide the leading terms:**
\[
\frac{-45x}{5x} = -9
\]
2. **Multiply the divisor by this result:**
\[
-9 \times (5x + 9) = -45x - 81
\]
3. **Subtract this from the original polynomial:**
\[
(-45x - 74) - (-45x - 81) = 7
\]
4. **Write the final answer:**
\[
-9 + \frac{7}{5x + 9}
\]
**Final Answer:**
\[
-9 + \frac{7}{5x + 9}
\]
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Simplify this solution Bonus Knowledge
To divide the polynomial \(-45x - 74\) by \(5x + 9\), we can use polynomial long division. 1. Divide the leading term: \(-45x \div 5x = -9\). 2. Multiply \(-9\) by the divisor \(5x + 9\): \(-9(5x + 9) = -45x - 81\). 3. Subtract this from the original polynomial: \((-45x - 74) - (-45x - 81) = 7\). Since \(7\) is the remainder, we can express the answer as: \[ -9 + \frac{7}{5x + 9} \] So, the final answer is \(-9\) with a remainder of \(\frac{7}{5x + 9}\).
