Polynomial Division Practice
Expand special products instantly, divide by long division and synthetic division, and use the Remainder Theorem. Fresh numbers every round.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss earns another hint; a third miss walks you through the full solution.
2 What you’ll practice
Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.
Square a binomial
(x + a)² and (x − a)² from the pattern.
Difference of squares
(x + a)(x − a) with no middle term.
Name the pattern
Perfect square or difference of squares?
Long division
Divide leading terms, multiply back, subtract.
Synthetic division
The fast lane for x − r divisors.
Remainder Theorem
The remainder is just f(r).
3 Watch out for these
The three mistakes students make most often on these problems.
(x + 5)² = x² + 25 misses the 10x. The pattern is a² + 2ab + b².
In long division, subtracting the partial product flips every sign.
A division answer is quotient AND remainder — R = 0 is the factor test.