Hi there,

(a)

let $\displaystyle f(X) = 2X^4 + 5X^3 + 8X^2 + 7X + 4$ and $\displaystyle g(X) = 2X^2 + 3X + 3$

the HCF(f, g) = 1.

but is there a special way to do this kind of question... or do i have to compute manually by long division?

(b)

now let $\displaystyle \alpha\epsilon C$ satisfy $\displaystyle f(\alpha) = 0$.

Find a,b,c,d $\displaystyle \epsilon Q$ such that :

$\displaystyle 1/g(\alpha) = a + b\alpha + c\alpha^2 + d\alpha^3$

any clue on how to go about with this one please? ill try it out for myself once i have an idea on what route to follow?

thnx a great deal guys