Calculator inputs
Example data table
| Mode | Example input | Expected factorization | Notes |
|---|---|---|---|
| Quadratic | 2x2 + 7x + 3 | (2x + 1)(x + 3) | Useful for a·c product-sum checks. |
| Difference of squares | 9x2 - 16 | (3x - 4)(3x + 4) | Recognize u2 - v2. |
| Sum of cubes | 8x3 + 27 | (2x + 3)(4x2 - 6x + 9) | Apply u3 + v3. |
| Common factor | 12x3 + 18x2 + 24x | 6x(2x2 + 3x + 4) | Extract the greatest shared coefficient and power. |
Formula used
For ax2 + bx + c, find factors of a·c whose sum is b. Then rewrite the middle term and factor by grouping.
u2 - v2 = (u - v)(u + v). The calculator also keeps square roots when values are not perfect squares.
u3 + v3 = (u + v)(u2 - uv + v2). u3 - v3 = (u - v)(u2 + uv + v2).
GCF = gcd(coefficients) × variablesmallest shared power. Pull that factor outside, then simplify the remaining polynomial.
How to use this calculator
- Select the factoring mode that matches your expression.
- Enter the coefficients, constant term, or term powers shown for that mode.
- Choose the variable symbol and graph range.
- Press Factor expression to place the result above the form.
- Review the factorization, method, roots, steps, and graph.
- Use the export buttons to save the summary as CSV or PDF.
FAQs
1. What expressions can this calculator handle?
It handles quadratics, difference-of-squares forms, sum-of-cubes forms, difference-of-cubes forms, and greatest common factor extraction for three-term expressions.
2. Does it only work with integers?
Integers give the cleanest symbolic factors. Decimal inputs still produce valid analysis, roots, graphing, and radical forms when exact integer binomials are unavailable.
3. Why does it sometimes say not factorable over integers?
Some polynomials have real roots but no integer binomial factorization. In that case, the tool shows exact real-root factor form or explains that no real linear factors exist.
4. What does the graph add to factoring?
The graph shows where the expression crosses or touches the x-axis. Those intercepts match real zeros and help confirm whether repeated or distinct real factors are present.
5. Can I use another variable besides x?
Yes. Enter a single letter in the variable symbol field. The result, formulas, and displayed factors will update to that chosen variable.
6. What does common factor mode do?
That mode extracts only the greatest common factor from three terms. It is helpful before applying grouping, quadratic methods, or pattern recognition manually.
7. Will the CSV file include every step?
The CSV export contains the main summary metrics such as mode, expression, factorization, roots, and method. The PDF export is better for keeping the full report.
8. Why are radicals shown in some answers?
Radicals appear when a square or cube term is not a perfect power. They keep the factorization exact instead of replacing it with rounded decimals.