Factoring Quadratics Generator
The Factoring Quadratics lesson organizes every trinomial-factoring technique into one decision process; this generator drills all of them, asking for one specific constant from the factored form every problem is built backward from.
How the difficulty levels work
| Difficulty | What it drills | Example |
|---|---|---|
| Easy | Leading coefficient of \(1\), find the smaller factor | \(x^{2}-2x-15=(x-5)(x+3)\), find \(-5\) |
| Medium | Difference of squares, or a perfect square trinomial | \(x^{2}-49=(x+7)(x-7)\), find \(7\) |
| Hard | The ac method, or a GCF pulled out first | Leading coefficient other than \(1\) |
Easy factors a trinomial with leading coefficient \(1\), asking for the smaller of the two constants.
Medium alternates between recognizing a difference of squares and a perfect square trinomial, two patterns worth spotting on sight.
Hard alternates between the ac method for a trinomial whose leading coefficient isn’t \(1\), and a trinomial that needs its GCF factored out first before the remaining leading-coefficient-of-\(1\) trinomial can be factored.
Using the generator
Pick a difficulty and a question count, and a fresh set appears instantly. Every answer here is a whole number, positive or negative — enter it exactly as computed.
- 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 |
|---|---|
| Leading coefficient \(1\) | Two numbers multiplying to \(c\), adding to \(b\) |
| Difference of squares | \(a^{2}-b^{2} = (a+b)(a-b)\) |
| Perfect square trinomial | \(a^{2}\pm 2ab+b^{2} = (a\pm b)^{2}\) |
| The ac method | Two numbers multiplying to \(ac\), adding to \(b\) |
See the Factoring Quadratics lesson for the full decision process and worked examples for every case.
Common mistakes to watch for
Skipping the GCF check. A trinomial with a shared numeric factor is far easier once that factor is removed first.
Forgetting the sign rules for the two numbers. A negative \(c\) always means the two numbers have opposite signs; a positive \(c\) means they share the sign of \(b\).
Misidentifying a perfect square trinomial. The middle term must equal exactly twice the product of the square roots of the first and last terms.
Finding a pair that adds to \(b\) but doesn’t multiply to \(ac\). Both conditions are required at the same time in the ac method.
Where to go next
For factoring beyond degree \(2\), the Factoring Higher-Degree Generator covers sum and difference of cubes and quadratic-in-form quartics. For the full decision process and every pattern, see the Factoring Quadratics lesson.