These comprehensive RBSE Class 8 Maths Notes Chapter 14 Factorization will give a brief overview of all the concepts.

→ When an algebraic expression can be written as the product of two or more expressions is called a factor of the given expression and this process of finding factors is called factorisation.

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

→ Factorisation when a conimon monomial factor occurs in each term:

Steps

- Find the HCF of all the terms of the given expression;
- Divide eath term by the HCF;
- Write the given expression as the product of the quotient obtained in step (2) and this HCF.

→ Factorisation by grouping:

Steps

- Arrange the terms of the given expression in groups in such a way that all the groups have a common factor;
- factorise each group:
- Take out the factor which is common to each group.

→ Factorisation when a binomial is common:

Steps

- Find the common binomial;
- Write the given expression as the product of this binomial and quotient obtained on dividing the given expression by this binomial.

→ Factorisation by using formulae:

- (a + b)
^{2}= (a + b)(a + b) = a^{2}+ b^{2}+ 2ab - (a - b)
^{2}= (a - b)(a - b) = a^{2}+ b^{2}- 2ab - (a + b)(a - b) = a
^{2}- b^{2} - (x + a)(x + b) = x
^{2}+ (a+b)x + ab - (a + b + c)
^{2}= (a + b + c)(a + b + c) = a^{2}+ b^{2}+ c^{2}+ 2ab + 2bc + 2ca - (a + b)
^{3}= (a + b)(a + b)(a + b) = a^{3}+ b^{3}+ 3ab (a + b) - (a - b)
^{3}= (a - b) (a - b) (a - b) = a^{3}- b^{3}- 3ab (a - b)

→ A monomial multiplied by a monomial always gives a monomial. But a monomial divided by a monomial may not give a monomial.

→ If the remainder is zero, both the divisor and the quotient, are factors of the dividend.

→ In case of divisions of algebraic expressions, we have Dividend = Divisor × Quotient + Remainder.

→ We know that in the case of numbers, division is the inverse of multiplication. This idea is applicable also to the division of algebraic expressions.

→ In the case of division of a polynomial by a monomial, we may carry out the divison 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 the common factors.

→ When you square a monomial, the co-efficient and each factor has to be squared.

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