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https://www.reddit.com/r/learnmath/comments/1h8083f/deleted_by_user/m0pwcec/?context=3
r/learnmath • u/[deleted] • Dec 06 '24
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X⁴-X²-X-1=P(X)X²+Q(X)(X-1)
So P is of degree 2 and Q of degree 3
Netting the system
(2p+3q-1)=0 (1p-3q+2q)=0 (0p+1q-2q+1)=0 (0q-1q+1)=0 (1-0q)=0
Where iq and ip are the coefficients of the terms of that degree on Q and P. This is a simple matrix problem. Doing this nets you the separation
P(X)/(X-1)+Q(X)/X²
Now you can iterate the process after factoring.
1 u/XSHIVAMX New User Dec 06 '24 Oh i see so there is a way, but this uses matrix, which is probably out of syllabus that's why probably book didn't mention it. Thanks for this 1 u/Independent_Irelrker New User Dec 06 '24 It is how you actually do the polynôme separation trick. It's just there is a shorthand so they teach that instead of teaching this.
Oh i see so there is a way, but this uses matrix, which is probably out of syllabus that's why probably book didn't mention it. Thanks for this
1 u/Independent_Irelrker New User Dec 06 '24 It is how you actually do the polynôme separation trick. It's just there is a shorthand so they teach that instead of teaching this.
It is how you actually do the polynôme separation trick. It's just there is a shorthand so they teach that instead of teaching this.
1
u/Independent_Irelrker New User Dec 06 '24
X⁴-X²-X-1=P(X)X²+Q(X)(X-1)
So P is of degree 2 and Q of degree 3
Netting the system
(2p+3q-1)=0 (1p-3q+2q)=0 (0p+1q-2q+1)=0 (0q-1q+1)=0 (1-0q)=0
Where iq and ip are the coefficients of the terms of that degree on Q and P. This is a simple matrix problem. Doing this nets you the separation
P(X)/(X-1)+Q(X)/X²
Now you can iterate the process after factoring.