Answers

2014-06-06T16:07:47+05:30
By Remainder theorem. if f(x) is divided by (x - a) then the remainder is f(a). 

Therefore,  if f(x) is divided by (ax + b) then the remainder is f(–b/a). 

If f(x) = 12x^3 - 13x^2 - 5x - 7 is divided by (3x + 2) then the remainder is f (\frac{-2}{3} )

 (\frac{-2}{3} ) = 12( \frac{-2}{3})^3 - 13 (\frac{-2}{3})^2 - 5( \frac{-2}{3}) - 7
                     
                          = 12( \frac{-8}{27}) - 13( \frac{4}{9}) +  \frac{10}{3} - 7
 
                          =  \frac{-32}{9} -  \frac{52}{9} +  \frac{10}{3} -  \frac{7}{1}

                          =  \frac{-32}{9} - \frac{52}{9} + \frac{30}{9} - \frac{63}{9}

                          =  \frac{-117}{9}
         
                          = –13

The remainder is –13

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