Factorise the following by using factor theorem. x 2 + 12 35 x + 1 35

Given polynomial is x 2 + 12 35 x + 1 35 . The above polynomial can be written as P x = x 2 + 12 35 x + 1 35 By factor theorem: A linear polynomial x - a is said to be factor of the polynomial P x , if P a = 0 . In the given polynomial coefficient of x 2 is 1 and the constant term is 1 35 . Hence the factors of 1 35 are ± 1 5 and ± 1 7 ⇒ P - 1 7 = - 1 7 2 + 12 35 - 1 7 + 1 35 = 1 7 5 - 12 + 7 35 = 0 Here, x = - 1 7 is the zero of the polynomial. So, x + 1 7 is a factor of the polynomial. Also, P - 1 5 = - 1 5 2 + 12 35 - 1 5 + 1 35 = 1 5 7 - 12 + 5 35 = 0 x = - 1 5 is also a zero of the polynomial. Therefore, x + 1 7 x + 1 5 are the factors of the given polynomial.

Factorise the following. 2 x 2 + 3 x + 2

Given that, We have to factorise 2 x 2 + 3 x + 2 by splitting middle term. The coefficient of middle term in the given polynomial is 3 . So, we split 3 into two parts such that their sum is 3 and product is 2 . The factors of 2 are 1 and 2 . Thus, the middle term will be split as 3 = 1 + 2 . ⇒ 2 x 2 + 3 x + 2 = 2 x 2 + x + 2 x + 2 = x 2 x + 1 + 2 2 x + 1 = 2 x + 1 x + 2 Therefore, the factors of 2 x 2 + 3 x + 2 are 2 x + 1 and x + 2 .