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Tool for Factorization of a polynomial. Factorizing consists in expressing a polynomial as a product, so it can be it's canonical form.

Answers to Questions

How to factorize a polynomial-like expression?

Factorizing a mathematical polynomial expression of nth degree means to express it as a product of polynomial factors.

Among the factorization's methods, the simplest is to recognize a remarkable identity

Example: The 2nd order polynomial \( a^2+2ab+b^2 \) is factorized as \( (a+b)^2 \)

Remarkables identities also apply with polynomials

Example: \( x^2+2x-a^2+1 = (-a+x+1)(a+x+1) \)

What is a remarkable identity?

A remarkable identity is an equality demonstrated between two mathematical terms, which is common enough to be detectable and usable without further demonstration. The best known are those used in factoring polynomials of degree 2:

$$ (a+b)^2 = a^2 + 2ab + b^2 $$

$$ (a-b)^2 = a^2 - 2ab + b^2 $$

$$ (a+b)(a-b)=a^2 - b^2 $$

What is an irreducible polynomial?

Irreducible polynomials are polynomials which cannot be decomposed into a product of two non-constant polynomials. 1st Degree polynomials are always irreducible.

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