SSC Sample Paper Mock Test-2 SSC CGL Tear-II Paper-1

What is remainder when \[12{{x}^{3}}-13{{x}^{2}}-5x+7\]is divided by\[(3x+2)\]is

A) 1

B) \[-\,\,1\]

C) 2

D) \[-\,\,2\]

Correct Answer: A

Solution :

Here, \[f(x)=12{{x}^{3}}-13{{x}^{2}}-5x+7\]

Put \[3x+2=0\]

\[\Rightarrow \] \[x=\frac{-2}{3}\]

\[f\left( \frac{-\,\,2}{3} \right)=12{{\left( \frac{-\,\,2}{3} \right)}^{3}}-13{{\left( \frac{-\,\,2}{3} \right)}^{2}}-5\times \frac{-\,\,2}{3}+7\]

\[=\frac{-96}{27}-\frac{52}{9}+\frac{10}{3}+7\]

\[=\frac{-\,\,32}{9}-\frac{52}{9}+\frac{10}{3}+7\]

\[=\frac{-\,\,32-52+30+63}{9}=\frac{-\,\,84+93}{9}=\frac{9}{9}=1\]