Step by Step
D
Divide
Divide the leading term of the dividend by the leading term of the divisor to get the next term of your answer (quotient).
M
Multiply
Multiply that quotient term by the entire divisor.
S
Subtract
Subtract the result from the current dividend — remember every sign in the bottom row flips when subtracting, so it's often easier to flip all the signs first, then add.
B
Bring down
Bring down the next term from the original dividend, then repeat the whole D-M-S-B cycle until the remainder's degree is less than the divisor's degree.
Applied Walkthrough
1
Divide (2x² + 6x + 4) by (x + 2). Divide: 2x² ÷ x = 2x — the first term of the quotient.
2
Multiply: 2x × (x + 2) = 2x² + 4x.
3
Subtract: (2x² + 6x) − (2x² + 4x) = 2x. (Flip every sign in the bottom row first: −2x² − 4x, then add.)
4
Bring down the 4: you now have 2x + 4. Repeat: divide 2x ÷ x = 2, multiply 2×(x+2) = 2x+4, subtract to get remainder 0. Final quotient: 2x + 2.
Exam Application
Exams test whether you can execute all four DMSB steps in the correct repeating cycle, and specifically whether you correctly flip every sign during the subtract step rather than just the first term.
⚠ Common Trap
The most common trap is a sign error during the Subtract step — every sign in the bottom row must flip, not just the first one. Some students find it easier to flip all the signs first, then add, rather than trying to subtract directly.
✓ Quick Self-Check
1. What does DMSB stand for?
Divide, Multiply, Subtract, Bring down.
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2. Divide (2x² + 6x + 4) by (x + 2).
2x + 2, with no remainder.
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3. What's the most common error during the Subtract step?
Only flipping the sign of the first term in the bottom row instead of every term.
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4. When do you stop the DMSB cycle?
When the remainder's degree is less than the divisor's degree.
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5. What technique helps avoid sign errors during Subtract?
Flip every sign in the bottom row first, then add instead of subtracting directly.
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