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Free factor by grouping calculator. Factor polynomials by grouping terms with step-by-step solutions and algebraic methods. Our calculator uses algebraic principles to determine all factoring relationships from any given polynomial.
Last updated: February 2, 2026
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x³ + 2x² + 3x + 6
Input polynomial
(x + 2)(x² + 3)
Factored form
Given expression: x³ + 2x² + 3x + 6
Group terms: (x³ + 2x²) + (3x + 6)
Factor out common factors: x²(x + 2) + 3(x + 2)
Factor by grouping: (x + 2)(x² + 3)
Result: (x + 2)(x² + 3)
Grouping
Group terms with common factors
Common Factor
Factor out common factors
Special Forms
Apply difference of squares formula
Method used
Grouping Method
Groups terms with common factors
Method used
Quadratic Grouping
Specialized for quadratic polynomials
Method used
Cubic Grouping
Specialized for cubic polynomials
Formula used
a² - b² = (a + b)(a - b)
Special factoring formula
Formula used
a³ + b³ = (a + b)(a² - ab + b²)
Special factoring formula
Features
Complete Analysis
Comprehensive algebraic calculations
For polynomial x³ + 2x² + 3x + 6:
Original
x³ + 2x² + 3x + 6
Factored
(x + 2)(x² + 3)
Our factor by grouping calculator uses the fundamental principles of algebraic factoring to factor polynomials by grouping terms with common factors. The calculation applies algebraic methods and factoring techniques to determine all polynomial relationships.
a² - b² = (a + b)(a - b)a³ + b³ = (a + b)(a² - ab + b²)a³ - b³ = (a - b)(a² + ab + b²)Grouping: ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)These formulas form the foundation of polynomial factoring and allow determination of all factoring relationships from any given polynomial. They apply to both simple and complex polynomial expressions.
Shows the factoring process from polynomial to factored form
Factoring by grouping is a fundamental algebraic technique used to factor polynomials with four or more terms. It's based on the principle of grouping terms with common factors, then factoring out the common factor from each group. This is essential for solving polynomial equations, simplifying expressions, and understanding algebraic relationships.
Need help with other algebraic calculations? Check out our polynomial calculator and equation solver.
Get Custom Calculator for Your PlatformResult: x³ + 2x² + 3x + 6 = (x + 2)(x² + 3)
The polynomial has been factored by grouping into the product of two factors.
x² + 5x + 6
Result: (x + 2)(x + 3)
x² - 4
Result: (x + 2)(x - 2)
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