Question

1/35+12/35a+a2 factorise

Answer 1

Given: The given quadratic polynomial : $\dfrac{1}{35}+\dfrac{12}{35}a+a^2$

To factorize the above polynomial.

Taking $\dfrac{1}{35}$ as common outside, we get

$\dfrac{1}{35}(1+12a+35a^2)$

$\text{Here, }1\timest35a^2=35a^2 =7a \times 5a$

$\text{also, }7a+5a=12a$

Then, $\dfrac{1}{35}(1+12a+35a^2)=\dfrac{1}{35}(1+7a+5a+35a^2)$

$=\dfrac{1}{35}(1(1+7a)+5a(1+7a))\\\\=\dfrac{1}{35}((1+7a)(1+5a))$[Taking (1+7a) as common]

Hence, the factorization of  $\dfrac{1}{35}+\dfrac{12}{35}a+a^2=\dfrac{1}{35}((1+7a)(1+5a))$ .