Factorization

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial.If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial.

Methods of Factorisation

(i) Common factors

(ii) By expressing as difference of squares

(iii) By grouping

(iv) Trinomials

(v) Sum or difference of cubes

Illustrations:

Type (i) By taking out common factors from all the terms of a polynomial

8a³ b - 6a²b² = 2a²b (4a - 3b)

Type (ii) By expressing the polynomial as the difference of two squares

121x² - 25y² = (11x)² - (5y)²

= (11x + 5y) (11x - 5y) [Using the identity a²-b²=(a-b)(a+b)]

Factorise: (5a + 6b)² - 49b²

Let x = 5a + 6b

Then the given expression

= (x)² - (7b)²

= (x + 7b) (x - 7b)

Re-substituting the value of x, we get

= [(5a + 6b + 7b)] [(5a + 6b) - 7b]

= (5a + 6b + 7b) (5a + 6b - 7b)

= (5a + 13b) (5a - b)