Write the dividend and divisor in descending powers of the variable
Divide the leading term of the dividend by the leading term of the divisor
Write the result as the first term of the quotient
Multiply the entire divisor by that term
Subtract the result from the current polynomial
Bring down the next term
Repeat the divide, multiply, subtract, and bring down steps
Continue until the remainder has a lower degree than the divisor
Write the quotient with the remainder over the divisor if needed
Check the result by multiplying the quotient by the divisor and adding the remainder