College Algebra / Unit 7 Alg 364 worked example, 60 to 90 seconds
Polynomial Long Division
The idea
Polynomial long division runs the arithmetic algorithm on terms — divide leading by leading, multiply back, subtract, repeat — and ends in the Division Algorithm: dividend equals divisor times quotient plus remainder.
In practice
Divide x³ − 3x + 2 by x − 1. Write the dividend with its missing term visible: x³ + 0x² − 3x + 2. Leading over leading: x³/x = x²; multiply back and subtract, leaving x² − 3x. Repeat: x²/x = x, subtract, leaving −2x + 2. Once more: −2x/x = −2, subtract — remainder 0. Quotient: x² + x − 2. The Division Algorithm is the receipt: (x − 1)(x² + x − 2) multiplies back to x³ − 3x + 2 exactly, and a zero remainder announces a clean factor.
Where people slip
Write missing-degree terms as zero terms; skipped columns wreck the subtraction.
Your place on the trail
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Unlocks
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