What is (m squared -7m-11) divided by (m-8) using long division

To divide \( m^2 - 7m - 11 \) by \( m - 8 \) using long division, follow these steps:

1. **Divide the first term**:
   Divide the leading term of the dividend \( m^2 \) by the leading term of the divisor \( m \).
   \[
   \frac{m^2}{m} = m
   \]
   So, the first term in the quotient is \( m \).

2. **Multiply**:
   Multiply \( m \) by \( m - 8 \):
   \[
   m \times (m - 8) = m^2 - 8m
   \]

3. **Subtract**:
   Subtract \( m^2 - 8m \) from \( m^2 - 7m - 11 \):
   \[
   (m^2 - 7m - 11) - (m^2 - 8m) = (-7m + 8m) - 11 = m - 11
   \]

4. **Divide again**:
   Divide the first term of the new expression \( m \) by \( m \):
   \[
   \frac{m}{m} = 1
   \]
   So, the next term in the quotient is \( 1 \).

5. **Multiply**:
   Multiply \( 1 \) by \( m - 8 \):
   \[
   1 \times (m - 8) = m - 8
   \]

6. **Subtract**:
   Subtract \( m - 8 \) from \( m - 11 \):
   \[
   (m - 11) - (m - 8) = -11 + 8 = -3
   \]

Thus, the quotient is:
\[
m + 1
\]
with a remainder of \( -3 \).

So, the final result is:
\[
m + 1 + \frac{-3}{m - 8}
\]

Would you like any additional details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you apply synthetic division to this problem?
2. What happens if the divisor is a binomial like \( m^2 - 8 \)?
3. How would the remainder change if the divisor was \( m + 8 \)?
4. Can you generalize this division method to higher degree polynomials?
5. How would you express the quotient and remainder as a mixed fraction?

**Tip**: In polynomial long division, always align terms of the same degree for easier subtraction during each step.

What is (m squared -7m-11) divided by (m-8) using long division?

Learn how to divide the polynomial m^2 - 7m - 11 by m - 8 using long division. This detailed solution walks you through each step, highlighting key algebraic concepts such as polynomial division and remainder. Ideal for students in Grades 9-10.

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