Factorize: 1 3 a 2 - 2 a - 9

Given: 1 3 a 2 - 2 a - 9 . The given quadratic polynomial can be written as follows: a 2 - 2 a × 3 - 9 × 3 3 = 1 3 a 2 - 6 a - 27 Comparing the given polynomial with standard quadratic polynomial a x 2 + b c + c . Here, a = 1 ; b = - 6 ; c = - 27 . Here we need to split the middle term b as sum or difference of two terms, whose product equals to a c . 1 3 a 2 - 9 - 3 a - 27 ⇒ 1 3 a 2 - 9 a + 3 a - 27 ⇒ 1 3 a a - 9 + 3 a - 9 ⇒ 1 3 a - 9 a + 3 ∴ 1 3 a 2 - 2 a - 9 = 1 3 a - 9 a + 3 .

Factorize: x 2 - 2 x + 3 4

Given: x 2 - 2 x + 3 4 . The given quadratic polynomial can be written as follows: 4 × x 2 - 4 × 2 x + 3 4 = 1 4 4 x 2 - 8 x + 3 Comparing the given polynomial with standard quadratic polynomial a x 2 + b c + c . Here, a = 4 ; b = - 8 ; c = 3 . Here we need to split the middle term b as sum or difference of two terms, whose product equals to a c . 1 4 4 x 2 - 6 + 2 x + 3 ⇒ 1 4 4 x 2 - 2 x - 6 x + 3 ⇒ 1 4 2 x 2 x - 1 - 3 2 x - 1 ⇒ 1 4 2 x - 1 2 x - 3 ∴ x 2 - 2 x + 3 4 = 1 4 2 x - 1 2 x - 3 .