Question

what must be added to polynomial p(x)=6x^5+5x^4+11x^3-3x^2+x+1 so that the result polynomial is exactly divisible by 3x^2-2x+4 ?

Answer 1

you just take out the remainder by dividing p(x) with 3x^2-2x+4
the remainder is -17x+13.....................1
now you just subtract this from p(x)
and than it will we divisible by 3x^2-2x+4
this is simple method 
the other method is
dividend=divisor*quotient+remainder
 you have remainder, divisor and have quotient 
so you can get dividend

Answer 2

We get remainder as -17x+13 and quotient as 2x^3+3x^2+3x-3.
if we subtract -17x+13 from 3x^2-2x+4 we get the ans....