Factor Polynomials by Grouping Calculator

Group terms, factor GCFs, and reveal matching binomials with clarity and control. Try smart regroupings that automatically align signs for common factors and binomials. Download CSV, generate PDF, and copy LaTeX for documentation, share your work. Fast, accurate grouping with clean, white interface design.

Enter Four Terms
Term 1
Format: c·x^e (e≥0). Integers only.
Term 2
Format: c·x^e (e≥0). Integers only.
Term 3
Format: c·x^e (e≥0). Integers only.
Term 4
Format: c·x^e (e≥0). Integers only.
Formula Used

Grouping rewrites a four-term polynomial as two groups, factors a greatest common factor in each group, and extracts a common binomial:

(A + B) + (C + D)
= GCF(A,B)·(a₁ + a₂) + GCF(C,D)·(a₃ + a₄)
= [G₁ + G₂] · (common binomial)

Here, GCF for monomials combines the integer greatest common divisor for coefficients and the minimum exponent for the variable. Signs may be flipped to align the common binomial.

How to Use
  1. Enter four terms using integer coefficients and non‑negative exponents.
  2. Pick a grouping manually or leave on Auto choose.
  3. Press Factor by Grouping to compute factors and steps.
  4. Use Copy LaTeX, Download CSV, or Download PDF for exports.
  5. Try the example table below to see common patterns.

Note: This tool targets single‑variable, integer‑coefficient polynomials. Different regroupings may be required to reveal the common binomial.

FAQs

A method for four-term polynomials: factor a GCF from two pairs of terms so the same binomial appears in both, then factor that binomial out.

Integers are supported. If you need rational or decimal handling via scaling and reduction, let me know and I can extend it.

Not all four-term polynomials factor by grouping. Try alternate groupings or check whether the common binomial exists. Some cases require different techniques.

Yes. Set the variable field to any single letter. All terms will use that symbol.

The tool chooses GCF signs to encourage matching binomials. If needed, it flips a group’s sign so the common binomial aligns across both groups.
Example Data

Click Load to populate the form.

# Polynomial (expanded) Factorization
1 x^3 + 3x^2 + 2x + 6 (x^2 + 2)(x + 3)
2 6x^2 + 9x + 4x + 6 (3x + 2)(2x + 3)
3 8x^3 + 12x^2 + 2x + 3 (4x^2 + 1)(2x + 3)
4 x^3 - 4x^2 + 3x - 12 (x^2 + 3)(x - 4)
5 4x^3 - 6x^2 + 10x - 15 (2x^2 + 5)(2x - 3)
Notes
  • All calculations run on submission; no internet required.
  • Use integers for coefficients; exponents must be ≥ 0.
  • Try different groupings if auto doesn’t find a match.

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