Without actual division, prove that 2x^{4}-5x^{3}-2x2 -x+2 is exactly divisible by x^{2}-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...