Start with the highest power
Write both polynomials in descending powers. Include a zero term for any missing power so that the columns line up. Divide the first term of the dividend by the first term of the divisor.
(x² + 5x + 6) ÷ (x + 2): x² ÷ x = x.
Multiply, subtract, repeat
Multiply x by the whole divisor to get x² + 2x. Subtract this from the dividend to leave 3x + 6. Then 3x ÷ x = 3. Subtract 3(x + 2) and the remainder is zero.
(x² + 5x + 6) ÷ (x + 2) = x + 3.
Check your answer
Multiply the quotient by the divisor and add the remainder. You should get back the original dividend.
(x + 3)(x + 2) = x² + 5x + 6.