Question

how to do this ...............?.

Answer 1

x^2-3x+2 can be written as (x-1)(x-2)
ie it has two roots 1 and 2
Now the bigger term (let it be f(x)) is divisible by it if it is divisible by both (x-1) and (x-2)
ie it should have 1 and 2 as it's root
Now check if f(1)=0 and f(2)=0
If they are then it is proved..

Answer 2

HEY FRIEND HERE'S YOUR ANSWER.
First let's factories
(x^2-3x+2)
on factorisation,you will get,
(x-1).(x-2)
now, apply, x=1 and x=2 in the equation 2x^4-6x^3+3x^2+3x-2.
In both the cases,you will get the reminder as 0 . Since it is divisible by both (x-1) and(x-2) it is also divisible by their product, x^2-3x+2 .SO WE HAVE PROVED THAT THE ABOVE EQUATION IS DIVISIBLE WITHOUT EVEN
ACTUALLY PERFORMING LONG DIVISION!
HOPE YOU FIND MY ANSWER HELPFUL.
WITH LUV AND CARE
LB..;)