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# gcd and polynomials watch

1. Find the greatest common divisor

d(x) of
f(x) = x^5 − 2x^4 − 3x^3 − 15x^2 + 10x + 25
and
g(x) = x^4 − 6x^2 − 24^x − 35

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using the polynomial long division

f(x) / g (x)

i ended up with 3x^3 + 135 x^2 -513x -815

couldn't factorise further !

---

the step after that

x^4 − 6x^2 − 24^x − 35 / 3x^3 + 135 x^2 -513x -815

and the answer was -13275x^2 -53578x+9150

but I don't know what should I do after that to get the gcd ,

and I'm not sure if my work is alright ..

any help ?

thnx
2. I get different answers - but it still leads to these polynomials being coprime (if that's the right word).

Are you certain you have the coefficients right?
3. By inspection, (x+1) is a factor of the quintic - I get (x^4 - 3x^3 - 15x + 1) as the other.

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Updated: February 5, 2010
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