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

Write the division problem:
___________ m  8  m^2  7m  11

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.

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

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

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

Bring down the next term:
 Bring down the 11 from the dividend.
m ___________ m  8  m^2  7m  11 (m^2  8m)  m  11

Repeat steps 25:
 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
 The remainder is 3.
The final result of dividing (m^2  7m  11) by (m  8) is:
m + 1  3/(m  8)