(m^2-7m-11) Divided By (m-8)

Jasonbradley

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Jun 16, 2024

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Dividing Polynomials: (m^2 - 7m - 11) ÷ (m - 8)

This article will guide you through the process of dividing the polynomial (m^2 - 7m - 11) by (m - 8) using polynomial long division.

Setting up the Division

1. Write the division problem:

       ___________
   m - 8 | m^2 - 7m - 11 
   

2. Focus on the leading terms:

   • The leading term of the divisor (m - 8) is m.
   • The leading term of the dividend (m^2 - 7m - 11) is m^2.

3. Determine the quotient term:

   • Ask yourself: "What do I need to multiply m by to get m^2?"
   • The answer is m. Write this above the line in the quotient section.

       m        
       ___________
   m - 8 | m^2 - 7m - 11 
   

4. Multiply the quotient term by the divisor:

   • Multiply m (the quotient term) by (m - 8):
   • m * (m - 8) = m^2 - 8m

5. Subtract:

   • Write the result (m^2 - 8m) below the dividend and subtract:

       m        
       ___________
   m - 8 | m^2 - 7m - 11 
           -(m^2 - 8m) 
           -------
               m - 11
   

Continuing the Division

6. Bring down the next term:

   • Bring down the -11 from the dividend.

       m        
       ___________
   m - 8 | m^2 - 7m - 11 
           -(m^2 - 8m) 
           -------
               m - 11 
   

7. Repeat steps 2-5:

   • Focus on the new leading term (m) in the dividend and the leading term (m) in the divisor.
   • What do you multiply m by to get m? The answer is 1. Write +1 in the quotient section.
   • Multiply 1 by (m - 8), giving (m - 8).
   • Subtract (m - 8) from the current dividend.

       m + 1     
       ___________
   m - 8 | m^2 - 7m - 11 
           -(m^2 - 8m) 
           -------
               m - 11 
               -(m - 8)
               -------
                     -3
   

The Result

8. The remainder is -3.

The final result of dividing (m^2 - 7m - 11) by (m - 8) is:

m + 1 - 3/(m - 8)