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# Factorization of Polynomials Using Algebraic Identities

## Summary

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HD 4:36

Factorisation

If g(x) and h(x) are two polynomials whose product is p(x). This can be written as p(x) = g(x) . h(x). g(x) and h(x) are called the factors of the polynomial p(x).

The process of resolving a given polynomial into factors is called factorisation. A non-zero constant is a factor of every polynomial.

Algebraic Identities

Polynomials can be factorised using algebraic identities.
A polynomial of degree two is called a quadratic polynomial. The identities used to factorise the quadratic polynomials are:

• (a + b)2 = a2 + 2ab + b2
• (a – b)2 = a2 – 2ab + b2
• a2 – b2 = (a + b)(a – b)
• (x + a)(x + b) = x2 + (a + b)x + ab
• (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

A polynomial of degree three is called a cubic polynomial. The algebraic identities used in factorising a cubic polynomial are:

• (a + b)3 = a3 + b3 + 3ab (a + b)
• (a – b)3 = a3 – b3 – 3ab (a – b)
• a3 + b3 = (a + b)(a2 – ab + b2)
• a3 – b3 = (a – b)(a2 + ab + b2)
• a3 + b3 + c– 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)

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