Question

On dividing f(x)=2x³+4x²+8x+9 by g(x) the quotient and remainder are 2x+4 and 2x-3 respectively. find g(x)

Answer 1

Answer:

         g(x) = x² + 3

Step-by-step explanation:

Given that

   f(x) / g(x)  =  2x+4  with a remainder of 2x-3

⇒ f(x)  =  (2x+4) g(x)  +  (2x-3)

⇒ g(x)  =  ( f(x) - 2x + 3 ) / ( 2x + 4 )

           = ( 2x³ + 4x² + 8x + 9 - 2x + 3 ) / ( 2x + 4 )

           = ( 2x³ + 4x² + 6x + 12 ) / ( 2x + 4 )

           = ( x³ + 2x² + 3x + 6 ) / ( x + 2 )

           = ( x²(x+2) + 3(x+2) ) / ( x + 2 )

           = x² + 3

Hope this helps!