# dividing complex polynomials

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#1
The question requires you to find the hcf/gcd of these polynomials: x^3 + 2ix + (1-x), and ix^3 - x^2 + 2, I`m trying to use long division, but the polynomials have the same degree, so I can factor out an i, but nothing else??
0
2 years ago
#2
(Original post by itlstallion69)
The question requires you to find the hcf/gcd of these polynomials: x^3 + 2ix + (1-x), and ix^3 - x^2 + 2, I`m trying to use long division, but the polynomials have the same degree, so I can factor out an i, but nothing else??
Not worked it out fully, but assume they have a common factor, z. For the two polynomails F and G, then (factor theorem)
F(z) = G(z) = 0
Does such a z exist? Note i(G(z)) will also be zero. From a quick sketch which probably contains some mistakes, there should be two such values, so the HCF is probably a quadratic and therefore the LCM will be a quartic.
Last edited by mqb2766; 2 years ago
0
2 years ago
#3
(Original post by itlstallion69)
The question requires you to find the hcf/gcd of these polynomials: x^3 + 2ix + (1-x), and ix^3 - x^2 + 2, I`m trying to use long division, but the polynomials have the same degree, so I can factor out an i, but nothing else??
The odd form of your first poly. - the (1-x) - together with the fact that Wolfram says the HCF is 1, makes me think there's a typo somewhere.
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#4
Sorry, the first polynomial ends in (1-i)
0
2 years ago
#5
https://www.wolframalpha.com/widgets...becb7c18d017e6
is still giving an HCF of 1? Do you have a picture of the question?
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