Polynomial Generator
Adding, subtracting, multiplying, and dividing polynomials are covered in full in the Polynomials lesson; this generator is where that skill turns into speed. Every problem asks you to evaluate a polynomial expression at a given value of \(x\) — you still have to combine or expand it correctly, but the final answer is always one checkable number.
How the difficulty levels work
| Difficulty | What it drills | Example |
|---|---|---|
| Easy | Evaluate a trinomial directly | \(x^{2}+5x+3\) at \(x=-4\) |
| Medium | Add or subtract two polynomials, then evaluate | \((P+Q)(2)\) |
| Hard | Multiply two binomials, or divide by a monomial, then evaluate | \((x+3)(x-2)\) at \(x=5\) |
Easy evaluates a single trinomial at a chosen integer \(x\) — direct substitution and order of operations.
Medium gives two polynomials, \(P(x)\) and \(Q(x)\), and asks for their sum or difference evaluated at a chosen \(x\) — combine like terms first, or evaluate each one separately and add; both reach the same answer.
Hard alternates between evaluating a product of two binomials (FOIL, then substitute) and evaluating the result of dividing a polynomial by a monomial — every division problem is built so it comes out exact, with no remainder.
Using the generator
Pick a difficulty and a question count, and a fresh set appears instantly. Every answer here is a whole number — negative results are common, so don’t forget the sign.
- Check Answers scores the set and flags exactly which problems need another look
- Show Answers reveals every solution, useful for reviewing a paper attempt
- Print Worksheet outputs a clean page for offline practice or classroom handouts
The rules this generator drills
| Rule | Statement |
|---|---|
| Combining like terms | Add or subtract coefficients only; the exponent never changes |
| Distributing a negative sign | \(-(a+b) = -a-b\), applied to every term when subtracting |
| Multiplying binomials | \((x+p)(x+q) = x^{2}+(p+q)x+pq\) |
| Dividing by a monomial | Divide every term separately |
See the Polynomials lesson for worked derivations of each of these, plus the special product patterns this generator doesn’t test directly.
Common mistakes to watch for
Forgetting to distribute the negative sign on a Medium subtraction problem. \((P-Q)(x)\) means every term of \(Q\) flips sign before adding — not just its first term.
Adding exponents when combining like terms. \(3x^{2}+5x^{2}=8x^{2}\), not \(8x^{4}\) — combining like terms only adds coefficients.
Substituting before simplifying the sign of a negative x. When \(x=-4\), \(x^{2}\) means \((-4)^{2}=16\), a positive number — a very common sign slip.
Dividing only the first term when dividing by a monomial. Every term in the numerator needs the same division applied to it.
Where to go next
Once these feel automatic, the Algebra Equation Generator shifts from evaluating expressions to solving for \(x\) directly. For the full reasoning and special product patterns behind every rule drilled here, see the Polynomials lesson.