Factor high-degree polynomials and find their roots.
Input Parameters
Try common forms like x^2 - 5x + 6 or x^3 - x to see the factorizer in action.
Analysis Results
(x - 2)(x - 3)
Factored Form
Results based on the provided expression
Roots2, 3
Polynomial Degree2
Quick Reference
Linearax + b
Quadraticax² + bx + c
Cubicax³ + bx² + cx + d
Quarticax⁴ + bx³ + cx² + dx + e
Factoring Higher-Degree Polynomials
Factoring a polynomial is the process of breaking it down into a product of simpler polynomials (factors). For higher-degree polynomials (degree ≥ 3), we often use the Rational Root Theorem, Synthetic Division, or factoring by grouping.
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Pro Tips
Rational Root Theorem: Check factors of the constant term divided by factors of the leading coefficient.
Descartes' Rule of Signs: Helps estimate the number of positive and negative real roots.
Remainder Theorem: If P(c) = 0, then (x - c) is a factor of P(x).
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Fun Facts
"The Fundamental Theorem of Algebra states that every non-zero polynomial of degree n has exactly n complex roots."
"Abel-Ruffini Theorem: There is no general algebraic formula (using radicals) to solve polynomials of degree 5 or higher."
"Factoring is essentially 'undoing' multiplication (the FOIL method for quadratics)."
