Factorisation

An irreducible factor is a factor that cannot be expressed further as a product of factors.

An expression with only one term is called a monomial. An expression with two terms is called a binomial.

An expression with one or more terms is called a polynomial. Thus a monomial, a binomial and a trinomial are all polynomials.

When we factorise an expression, we write it as a product of factors. These factors may be numbers, algebraic variables or algebraic expressions.

In the case of division of a polynomial by a monomial, we may carry out the division either by dividing each term of the polynomial by the monomial or by the common factor method.

In the case of division of a polynomial by a polynomial, we cannot proceed by dividing each term in the dividend polynomial by the divisor polynomial. Instead, we factorise both the polynomials and cancel their common factors.

Factors of an algebraic expression are the expressions which we multiply to get that expression. The process of finding expressions whose product is the given expression is called factorisation. Square of a binomial is called perfect square trinomial. An algebraic expression having three terms is called a trinomial. Algebraic identities
  • a2 + 2ab + b2 = (a + b)2
  • a2 - 2ab + b2 = (a - b)2
  • a2 – b2 = (a + b)(a – b)
  • x2 + (a + b)x + ab = (x + a)(x + b)

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