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

Set up the division problem:
_______ m  8  m²  7m  11

Divide the leading terms:
 m² divided by m is m. Write "m" above the line.
m_______ m  8  m²  7m  11

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

Subtract:
 Subtract (m²  8m) from (m²  7m). Notice that the m² terms cancel out.
m_______ m  8  m²  7m  11 m²  8m  m

Bring down the next term:
 Bring down the "11" from the dividend.
m_______ m  8  m²  7m  11 m²  8m  m  11

Repeat steps 25:
 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

Subtract again:
 Subtract (m  8) from (m  11).
m + 1____ m  8  m²  7m  11 m²  8m  m  11 m  8  3

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.