Polynomial long division works just like number long division — divide, multiply, subtract, bring down.
Try it
(x² + 5x + 6) ÷ (x + 2)
x² ÷ x = x. Multiply: x(x+2) = x² + 2x. Subtract: 3x + 6. 3x ÷ x = 3. Multiply: 3(x+2) = 3x + 6. Subtract: 0. Answer: x + 3.