Polynomial long division works just like number long division — divide, multiply, subtract, bring down.
Walk through
Step 1 of 5
Set up
Divide x² + 5x + 6 by x + 2 — same rhythm as number long division: divide, multiply, subtract, bring down.
Keep terms lined up by degree, and write a 0 placeholder for any missing power (e.g. x³ + 1 = x³ + 0x² + 0x + 1) so columns don't drift.
Your turn
Divide x² + 7x + 10 by x + 5.
Watch out
When you subtract, subtract the whole product — every term changes sign. Forgetting to flip the sign on the second term is the #1 long-division slip.
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.