Let f(x) = 2x^4 + 5x^3 + 8x^2 + 7x + 4

g(x) = 2x^2 + 3x + 3

Show that hcf (f,g) = 1

I used the long division of polynomial and found out:

f(x) = (x^2 + x +1)(2x^2 + 3x +3) + (x +1)

do it again, we get

2x^2 + 3x + 3 = (2x + 1)(x + 1) +2

So hcf (f,g) = 2

I dont know why I got the wrong answer, it's supposed to be 1 and i have checked many times but it doesnt work. Please help me, thanks very much