RBSE Class 8 Maths Notes Chapter 14 Factorization

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

RBSE Class 8 Maths Chapter 14 Notes Factorization

→ 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

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

→ Factorisation by grouping:
Steps

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

→ Factorisation when a binomial is common:
Steps

1. Find the common binomial;
2. 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) = a² + b² + 2ab
• (a - b)² = (a - b)(a - b) = a² + b² - 2ab
• (a + b)(a - b) = a² - b²
• (x + a)(x + b) = x² + (a+b)x + ab
• (a + b + c)² = (a + b + c)(a + b + c) = a² + b² + c² + 2ab + 2bc + 2ca
• (a + b)³ = (a + b)(a + b)(a + b) = a³ + b³ + 3ab (a + b)
• (a - b)³ = (a - b) (a - b) (a - b) = a³ - b³ - 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.