Factorize:$ 2 x^{2}-\frac{5}{6} x+\frac{1}{12} $
Given :
\( 2 x^{2}-\frac{5}{6} x+\frac{1}{12} \)
To do :
We have to factorize the given expression.
Solution :
$2 x^{2}-\frac{5}{6} x+\frac{1}{12}=2 x^{2}-\frac{1}{2} x-\frac{1}{3} x+\frac{1}{12}$
$=x(2 x-\frac{1}{2})-\frac{1}{6}(2 x-\frac{1}{2})$ [Since $\frac{1}{6}=\frac{-1}{2} \times \frac{-1}{3}, \frac{-5}{6}=\frac{-1}{2}-\frac{1}{3}$]
$=(2 x-\frac{1}{2})(x-\frac{1}{6})$
Hence, $2 x^{2}-\frac{5}{6} x+\frac{1}{12}=(2 x-\frac{1}{2})(x-\frac{1}{6})$.
Related Articles
- Factorize:\( x^{2}+\frac{12}{35} x+\frac{1}{35} \)
- Factorize:\( \left(x^{2}+\frac{1}{x^{2}}\right)-4\left(x+\frac{1}{x}\right)+6 \)
- Take away:\( \frac{6}{5} x^{2}-\frac{4}{5} x^{3}+\frac{5}{6}+\frac{3}{2} x \) from \( \frac{x^{3}}{3}-\frac{5}{2} x^{2}+\frac{3}{5} x+\frac{1}{4} \)
- $\frac{x-1}{2}+\frac{2 x-1}{4}=\frac{x-1}{3}-\frac{2 x-1}{6}$.
- Solve: \( \frac{x}{2}-\frac{1}{4}\left(x-\frac{1}{3}\right)=\frac{1}{6}(x+1)+\frac{1}{12} \)
- Add the following algebraic expressions(i) \( 3 a^{2} b,-4 a^{2} b, 9 a^{2} b \)(ii) \( \frac{2}{3} a, \frac{3}{5} a,-\frac{6}{5} a \)(iii) \( 4 x y^{2}-7 x^{2} y, 12 x^{2} y-6 x y^{2},-3 x^{2} y+5 x y^{2} \)(iv) \( \frac{3}{2} a-\frac{5}{4} b+\frac{2}{5} c, \frac{2}{3} a-\frac{7}{2} b+\frac{7}{2} c, \frac{5}{3} a+ \) \( \frac{5}{2} b-\frac{5}{4} c \)(v) \( \frac{11}{2} x y+\frac{12}{5} y+\frac{13}{7} x,-\frac{11}{2} y-\frac{12}{5} x-\frac{13}{7} x y \)(vi) \( \frac{7}{2} x^{3}-\frac{1}{2} x^{2}+\frac{5}{3}, \frac{3}{2} x^{3}+\frac{7}{4} x^{2}-x+\frac{1}{3} \) \( \frac{3}{2} x^{2}-\frac{5}{2} x-2 \)
- Solve the following:$\frac{1}{x-2}+\frac{2}{x-1}=\frac{6}{x}$
- Factorize:\( 21 x^{2}-2 x+\frac{1}{21} \)
- Solve: \( \frac{x+5}{2}=1+\frac{2 x-1}{3} \).
- Take away:(i) \( \frac{6}{5} x^{2}-\frac{4}{5} x^{3}+\frac{5}{6}+\frac{3}{2} x \) from \( \frac{x^{3}}{3}-\frac{5}{2} x^{2}+ \) \( \frac{3}{5} x+\frac{1}{4} \)(ii) \( \frac{5 a^{2}}{2}+\frac{3 a^{3}}{2}+\frac{a}{3}-\frac{6}{5} \) from \( \frac{1}{3} a^{3}-\frac{3}{4} a^{2}- \) \( \frac{5}{2} \)(iii) \( \frac{7}{4} x^{3}+\frac{3}{5} x^{2}+\frac{1}{2} x+\frac{9}{2} \) from \( \frac{7}{2}-\frac{x}{3}- \) \( \frac{x^{2}}{5} \)(iv) \( \frac{y^{3}}{3}+\frac{7}{3} y^{2}+\frac{1}{2} y+\frac{1}{2} \) from \( \frac{1}{3}-\frac{5}{3} y^{2} \)(v) \( \frac{2}{3} a c-\frac{5}{7} a b+\frac{2}{3} b c \) from \( \frac{3}{2} a b-\frac{7}{4} a c- \) \( \frac{5}{6} b c \)
- Solve: $\frac{4 x-5}{6 x+3}=\frac{2 x-5}{3 x-2}$.
- Solve:$x^{\frac{1}{2}}$; by $x^{\frac{5}{2}}$
- Factorize:\( \frac{8}{27} x^{3}+1+\frac{4}{3} x^{2}+2 x \)
- Solve the following system of equations:$\frac{5}{x-1} +\frac{1}{y-2}=2$$\frac{6}{x-1}-\frac{3}{y-2}=1$
- Solve the following pairs of equations by reducing them to a pair of linear equations:(i) \( \frac{1}{2 x}+\frac{1}{3 y}=2 \)\( \frac{1}{3 x}+\frac{1}{2 y}=\frac{13}{6} \)(ii) \( \frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2 \)\( \frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1 \)(iii) \( \frac{4}{x}+3 y=14 \)\( \frac{3}{x}-4 y=23 \)(iv) \( \frac{5}{x-1}+\frac{1}{y-2}=2 \)\( \frac{6}{x-1}-\frac{3}{y-2}=1 \)(v) \( \frac{7 x-2 y}{x y}=5 \)\( \frac{8 x+7 y}{x y}=15 \),b>(vi) \( 6 x+3 y=6 x y \)\( 2 x+4 y=5 x y \)4(vii) \( \frac{10}{x+y}+\frac{2}{x-y}=4 \)\( \frac{15}{x+y}-\frac{5}{x-y}=-2 \)(viii) \( \frac{1}{3 x+y}+\frac{1}{3 x-y}=\frac{3}{4} \)\( \frac{1}{2(3 x+y)}-\frac{1}{2(3 x-y)}=\frac{-1}{8} \).
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies