(m 2 − 7m − 11) ÷ (m − 8)

Jasonbradley

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Jun 16, 2024

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Dividing Polynomials: (m² - 7m - 11) ÷ (m - 8)

This article will guide you through the process of dividing the polynomial (m² - 7m - 11) by (m - 8) using long division.

Steps for Long Division

1. Set up the division problem:

        _______
   m - 8 | m² - 7m - 11 
   

2. Divide the leading terms:

   • m² divided by m is m. Write "m" above the line.

        m_______
   m - 8 | m² - 7m - 11 
   

3. Multiply the divisor (m - 8) by the quotient term (m):

   • (m - 8) * m = m² - 8m. Write this result below the dividend.

        m_______
   m - 8 | m² - 7m - 11 
          m² - 8m 
   

4. Subtract:

   • Subtract (m² - 8m) from (m² - 7m). Notice that the m² terms cancel out.

        m_______
   m - 8 | m² - 7m - 11 
          m² - 8m 
          -------
               m 
   

5. Bring down the next term:

   • Bring down the "-11" from the dividend.

        m_______
   m - 8 | m² - 7m - 11 
          m² - 8m 
          -------
               m  - 11 
   

6. Repeat steps 2-5:

   • Divide the new leading term (m) by the divisor's leading term (m): m / m = 1. Write "+ 1" next to the "m" in the quotient.
   • Multiply (m - 8) by 1: (m - 8) * 1 = m - 8. Write this below the "m - 11".

        m + 1____
   m - 8 | m² - 7m - 11 
          m² - 8m 
          -------
               m  - 11 
               m  - 8
   

7. Subtract again:

   • Subtract (m - 8) from (m - 11).

        m + 1____
   m - 8 | m² - 7m - 11 
          m² - 8m 
          -------
               m  - 11 
               m  - 8
               -------
                    -3
   

8. The remainder is -3:

   • The final result is m + 1 with a remainder of -3. We can write this as: (m² - 7m - 11) ÷ (m - 8) = m + 1 - 3/(m - 8)

Conclusion

By applying long division, we successfully divided the polynomial (m² - 7m - 11) by (m - 8) and arrived at the quotient m + 1 with a remainder of -3.