(m^2-7m-11)/(m-8)

Jasonbradley

3 min read

·

Jun 16, 2024

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Simplifying the Expression (m^2 - 7m - 11)/(m - 8)

This expression represents a rational function, a fraction where the numerator and denominator are polynomials. Simplifying it involves dividing the numerator by the denominator. There are two primary approaches:

1. Polynomial Long Division

Steps:

1. Set up the division:

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

2. Divide the leading terms:

   • m into m^2 goes m times.
   • Write 'm' above the line.

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

3. Subtract:

   • Subtract the entire line below.

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

4. Bring down the next term:

   • Bring down '-11'.

5. Repeat the process:

   • m into m goes 1 time.
   • Write '+1' above the line.

        m + 1 _______
   m - 8 | m^2 - 7m - 11
           m^2 - 8m
           -------
               m - 11
               m - 8
               -------
                  -3
   

6. The result:

   • The simplified form is: m + 1 - 3/(m - 8)

2. Factoring

While the numerator does not factor easily, this method could be used if it did.

Steps:

1. Factor the numerator (if possible):

   • In this case, the numerator does not factor easily using standard techniques.

2. Cancel common factors:

   • If there were any common factors, they would be cancelled from both numerator and denominator.

Conclusion

The simplified form of the expression (m^2 - 7m - 11)/(m - 8) is m + 1 - 3/(m - 8). This is obtained through polynomial long division. Factoring is not applicable in this specific case due to the numerator's lack of easily identifiable factors.