As your given polynomial is of degree 2 by the theorem th-cam.com/video/IyEIkOWApwk/w-d-xo.html If this polynomial of Degree 2 has root then it is reducible if it has not root then it is Irreducible over Base field... Here it has √2i and -√2i these two roots are not present in R it is maginary roots which is present in C. We conclude that roots are not present in R so by theorem given polynomial is Irreducible over R. And As roots are present in C so therefore by theorem given Polynomial is reducible over C. I Hope this help you , if u still have any query plz let me know in comment ....
Sir plz make videos on theorem of chapter algebraic extension of fileds in ADVANCE ABSTRACT ALGEBRA
Thank you so much..last example helped alot👍
Thank you Sir ❤️ your video is Very much helpful 😊
Glad to hear that
Good explanation
X^4+3x^2+2 me p=3 rakhne per irreducile q nahi hua???
Sir quotient ring par video dal dijiye
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Mashallah good ho gya
In last example why we cannot use mod p test
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If a polynomial x²+1 given over Q(i)[x] is reducible or irreducible? Plz answer
Yes it is reducible over field Q(i). Because all roots exist in Q(I).....
Thnku sir
The polynomial f(x) =2x^2+4 is irreducible over R but reducible over C why?
As your given polynomial is of degree 2 by the theorem th-cam.com/video/IyEIkOWApwk/w-d-xo.html
If this polynomial of Degree 2 has root then it is reducible if it has not root then it is Irreducible over Base field...
Here it has √2i and -√2i these two roots are not present in R it is maginary roots which is present in C. We conclude that roots are not present in R so by theorem given polynomial is Irreducible over R. And
As roots are present in C so therefore by theorem given Polynomial is reducible over C.
I Hope this help you , if u still have any query plz let me know in comment ....
Thank you very much.
Sir,x^4+x^2+1 in Z2 is reducible or irreducible...??please tell
It is reducible
Thanks
Welcome !!!!!!
By einestain criteria
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Wow helpful video
Thanks for liking
Great amazing
1st
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