Factorization

Factorization of whole number A number that divides another number exactly without leaving remainder is called a factor. For example, 2 is a factor of 8, because 2 divides 8 without leaving a remainder. Step to find all factor of a whole number Example: Find all the factors of 20. Start at 1 : 20 = 1 x 20 Then go to 2 : 20 = 2 x 10 Then go to 3 : 3 is not a factor of 20 Then go to 4 : 20 = 4 x 5 Since there is no whole number between 4 and 5, We have found all factors of 20. Factors of 20 are 1 , 2 , 4 , 5 , 10 and 20

Factorization of whole number with variable The process of expressing any polynomial as a product of its factors is called factorization. We can express the following algebraic expressions as the product of their factors: 6x3 14x2 14 6 x2 x3 2 7 x x 2 3 x x x x x x x Factor of 14x2 = 2x x 7x Factor of 6x3 = 2x2 x 3x

Factorization by taking common factor In this method, we rewrite the expression with the common factors outside brackets. Remember that common factors of two or more terms are factors that appear in all the terms. Example 1: Factorize 2x + 6 Solution Factors of 2x = 2 x x Factors of 6 = 2 x 3 Common factor = 2 Write the common factor 2 outside and leave remaining inside the bracket 2x + 6 = 2 x x + 2 x 3 = 2 (x + 3) (ans)

4x2 + 20x = 2 x 2 x x x x + 2 x 2 x 5 x x = 2 x 2 x x (x + 5) Example2: Factorize 4x2+ 20x Solution Factors of 4x2 = 2 x 2 x x x x Factors of 20x = 2 x 2 x 5 x x Common factor = 2 x 2 x x = 4 x Write the common factor 4x outside and leave remaining inside the bracket 4x2 + 20x = 2 x 2 x x x x + 2 x 2 x 5 x x = 2 x 2 x x (x + 5) = 4x (x + 5 ) (ans)

Solution a2b + ab2 = a x a x b + a x b x b = ab(a + b) (ans) Example3: Factorize a2b + ab2 Solution Factors of a2b = a x a x b Factors of ab2 = a x b x b Common factor = a x b = ab Write the common factor ab outside and leave remaining inside the bracket a2b + ab2 = a x a x b + a x b x b = ab(a + b) (ans)

Try These Factorize the following: 5x – 10 15xy2 + 25x2y