Question

Factorize 2x² − $\frac{5}{6}x+\frac{1}{12}$.

Answer 1

Splitting middle term of $2x^2-\frac{5}{6}x+\frac{1}{12}$, we get
$$\begin{gathered} 2x^2-\frac{5}{6}x+\frac{1}{12}=2x^2-\frac{1}{2}x-\frac{1}{3}x+\frac{1}{12}\left(\because \frac{1}{2}+\frac{1}{3}=\frac{5}{6},\frac{1}{2}\times \frac{1}{3}=\frac{1}{6}\right) \\ =2x\left(x-\frac{1}{4}\right)-\frac{1}{3}\left(x-\frac{1}{4}\right) \\ =\left(x-\frac{1}{4}\right)\left(2x-\frac{1}{3}\right) \end{gathered}$$
Hence, the required factorisation is $\left(x-\frac{1}{4}\right)\left(2x-\frac{1}{3}\right)$.