Question

when polynomial 2xcube+3xsquare+ax+b is divided by x-2 leaves remaider 2 and x+2 leaves remainder -2 find a and b

Answer 1

x-2√2x3+3x2+ax+b
      -2x3+4x2
               -x2+ax
               -x2+4x
                 
4x+ax+b=2\
do same with other x+2
and substitute values of a from here in it

Answer 2

Here ,
2x^3 +3x^2 +ax+b -2 = 0, as by dividing this equation by x-2 it leaves remainder 2 so i subtract 2 from it.
Now, by putting x= 2
2a+b = -26
Again doing the same process ,
2x^3 +3x^2 +ax+b +2= 0,
By putting x= -2
-2a+b= 2
By solving both the equations
a= -7
b= -12