Factorization of Polynomials Using Algebraic Identities

Summary

Algebraic identities of second degree

  • (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


These identities can be used to factorise quadratic polynomials. A polynomial is said to be cubic polynomial if its degree is three. Cubic polynomials can be factorised using factor theorem. The algebraic identities used in factorising a third degree 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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