Thread: hcf of long division polynomial

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

There's nothing wrong with that calculation. But remember that the gcd (or hcf) of two polynomials is usually defined as the monic polynomial of highest degree that divides both of them. Your answer 2 is not monic because the highest degree term (the constant term!) has coefficient 2.

To get the right answer, divide it by 2. (!)