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Polynomial Factorization

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

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Polynomial Factorization -

Tag(s) : Mathematics, Symbolic Computation

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# Polynomial Factorization

## Factorization of polynomials

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

### How to factorize a polynomial-like expression?

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

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

Example: $$a^2+2ab+b^2$$ 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.