Without actual division, prove that 2x4-5x3-2x2 -x+2 is exactly divisible by x2-3x+2
by splitting x^2-3x+2, we got=
x^2 -2x -1x +2
x(x-2)-1(x-2)
(x-1)(x-2)
so, x=1 & x=2
then, by putting 1 in f(x)
it will be 0
& putting 2 in f(x)
it will again be 0
so it's proved...