Polynomial Factoring Calculator
Enter any single-variable polynomial to detect common factors, rational roots, and classical factorization patterns step by step.
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Related knowledge
Definition of factorization
Factorization rewrites a polynomial as a product of simpler expressions (factors) within a number system, which is helpful for solving equations and simplifying algebraic manipulations.
How factorization helps
- Solve polynomial equations quickly by setting each factor to zero.
- Simplify algebraic expressions and rational functions before further operations.
- Reveal structure such as repeated roots or symmetry for optimization problems.
Strategy tips
Start by extracting common factors, then test for recognizable patterns (squares, cubes, grouping) before searching for rational roots.
Classical formulas
Perfect cube
a³ + 3a²b + 3ab² + b³ = (a + b)³
Example: x³ + 3x² + 3x + 1 = (x + 1)³.
Difference of squares
a² - b² = (a + b)(a - b)
Example: x² - 4 = (x + 2)(x - 2).
Perfect square trinomials
a² ± 2ab + b² = (a ± b)²
Example: x² + 6x + 9 = (x + 3)².
Grouping method
Group terms that share a factor, factor each group, then factor the common binomial.
Example: ax + ay + bx + by = (a + b)(x + y).
Common factor extraction
Pull out the greatest common factor before applying other techniques.
Example: 3x² + 6x = 3x(x + 2).