To simplify the expression \(\frac{3m^3 - 7m^2 - 26m + 10}{-5 + 3m}\), we will use polynomial long division.

### Step-by-Step Solution:

1. **Rewrite the expression:**
   \[
   \frac{3m^3 - 7m^2 - 26m + 10}{3m - 5}
   \]
   Note: I have rearranged the divisor to match the polynomial standard form order.

2. **Perform polynomial long division:**

   Divide \(3m^3 - 7m^2 - 26m + 10\) by \(3m - 5\):

   - **First term:** Divide the leading term of the numerator by the leading term of the divisor:  
     \[
     \frac{3m^3}{3m} = m^2
     \]
     
   - **Multiply:** \(m^2 \times (3m - 5) = 3m^3 - 5m^2\)
     
   - **Subtract:** Subtract this from the original polynomial:  
     \[
     (3m^3 - 7m^2 - 26m + 10) - (3m^3 - 5m^2) = -2m^2 - 26m + 10
     \]

   - **Next term:** Divide the leading term of the new polynomial by the leading term of the divisor:  
     \[
     \frac{-2m^2}{3m} = -\frac{2}{3}m
     \]
     
   - **Multiply:** \(-\frac{2}{3}m \times (3m - 5) = -2m^2 + \frac{10}{3}m\)
     
   - **Subtract:**  
     \[
     (-2m^2 - 26m + 10) - (-2m^2 + \frac{10}{3}m) = -\frac{88}{3}m + 10
     \]

   - **Final term:** Divide the leading term of the new polynomial by the leading term of the divisor:  
     \[
     \frac{-\frac{88}{3}m}{3m} = -\frac{88}{9}
     \]

   - **Multiply:** \(-\frac{88}{9} \times (3m - 5) = -\frac{88}{3}m + \frac{440}{9}\)
     
   - **Subtract:**  
     \[
     \left(-\frac{88}{3}m + 10\right) - \left(-\frac{88}{3}m + \frac{440}{9}\right) = 10 - \frac{440}{9} = \frac{90}{9} - \frac{440}{9} = -\frac{350}{9}
     \]

   The remainder is \(-\frac{350}{9}\).

### Final Answer:

The result of the division is:
\[
m^2 - \frac{2}{3}m - \frac{88}{9} + \frac{-\frac{350}{9}}{3m - 5}
\]

or more compactly:
\[
m^2 - \frac{2}{3}m - \frac{88}{9} - \frac{350}{9(3m - 5)}
\]

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. How does polynomial long division work in more detail?
2. What is the significance of finding a remainder in polynomial division?
3. Can you always divide two polynomials like this?
4. What are some applications of polynomial division in real life?
5. How does this relate to synthetic division, and when can that be used?

**Tip:** When dividing polynomials, aligning like terms and carefully performing arithmetic operations step-by-step are key to avoiding errors.

Learn how to simplify the expression (3m^3 - 7m^2 - 26m + 10) / (-5 + 3m) using polynomial long division with a detailed step-by-step solution. This problem involves dividing polynomials and understanding polynomial long division methods. Suitable for advanced high school students.

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