Factorize:$ x^{2}+\frac{12}{35} x+\frac{1}{35} $

Given :

\( x^{2}+\frac{12}{35} x+\frac{1}{35} \)

To do :

We have to factorize the given expression.

Solution :

$x^{2}+\frac{12}{35} x+\frac{1}{35}=x^{2}+\frac{1}{5} x+\frac{1}{7} x+\frac{1}{35}$                     [Since $\frac{1}{35}=\frac{1}{5} \times \frac{1}{7}, \frac{12}{35}=\frac{1}{5}+\frac{1}{7}$]

$=x(x+\frac{1}{5})+\frac{1}{7}(x+\frac{1}{5})$

$=(x+\frac{1}{5})(x+\frac{1}{7})$

Hence, $x^{2}+\frac{12}{35} x+\frac{1}{35}=(x+\frac{1}{5})(x+\frac{1}{7})$.

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Updated on: 10-Oct-2022

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