Polynomial Division Game
Find the quotient coefficients and remainder when dividing quadratic expressions.
Choose Practice or Daily to begin.
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Instructions, device progress and accessibility
Choose Easy, Normal or Hard and select Practice or a daily puzzle based on the UTC date. Enter answers or choose a correction, then select Check answer. Hints and Undo mark a round as assisted. Best scores and progress are stored only in this browser; no account is needed.
Local progress is checked when play begins.
How to play Polynomial Division
Read the quadratic dividend and linear divisor, then enter the coefficient of x, the quotient constant and the remainder. Check all three fields. Easy rounds use a zero remainder; other levels include nonzero remainders.
Worked example
Example: (x² + 5x + 6) ÷ (x + 2) = x + 3 with remainder 0. Multiplying (x + 2)(x + 3) returns the original quadratic.
Math formulas and key skills
Dividend = Divisor × Quotient + Remainder. For division by x − r, synthetic division evaluates the coefficient sequence at r.
Avoid common mistakes
Remember that the synthetic divisor value r is the root of x − r. For x + 2, use r = −2, not +2.
Frequently asked questions
What is a remainder in polynomial division?
The leftover constant after the divisor times the quotient is subtracted from the dividend.
How can I check my answer?
Multiply the divisor by the quotient, add the remainder and compare coefficients with the starting polynomial.