greatest common divisor

[dhiraj]

find 'c' if gcd of x^3+cx^2-x+2c & x^2+cx-2 is a linear polynomial.

what i did is presented below:

let f(x) = x^3 + cx^2 - x + 2c and g(x) = x^2 + cx - 2.
further let h(x) = ax+b is the linear [URL="http://freemathhelp.com/polynomials.html"]polynomial which is the gcd of f(x) and g(x).

now since h(x) divides g(x), so h(x) will also divide x*g(x).

h(x) will also divide f(x)-g(x) [using gcd of two numbers also divides their difference].

so h(x) will also divide f(x)-x*g(x) i.e. h(x) will divide x+2c.

now what? please suggest. is there any flaw in the methodology adopted here?
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[dhiraj]

find 'c' if gcd of x^3+cx^2-x+2c & x^2+cx-2 is a linear polynomial.

What i did is presented below:

Let f(x) = x^3 + cx^2 - x + 2c and g(x) = x^2 + cx - 2.
Further let h(x) = ax+b is the linear [url="http://freemathhelp.com/polynomials.html"]polynomial which is the gcd of f(x) and g(x).

Now since h(x) divides g(x), so h(x) will also divide x*g(x).

H(x) will also divide f(x)-g(x) [using gcd of two numbers also divides their difference].

So h(x) will also divide f(x)-x*g(x) i.e. H(x) will divide x+2c.

Now what? Please suggest. Is there any flaw in the methodology adopted here?
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somebody please help...