What is the need of zero polynomial? [closed]












-2














Someday while reading about polynomials (from: https://en.m.wikipedia.org/wiki/Polynomial), i came across with a topic, zero polynomial. It writes as:




enter image description here




My question: what is the need to introduce zero polynomial in mathematics?










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closed as off-topic by Did, Cesareo, Martín Vacas Vignolo, Eevee Trainer, Leucippus Dec 31 '18 at 2:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Did, Cesareo, Martín Vacas Vignolo, Eevee Trainer, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.









  • 6




    When I add two polynomials, I like to get a polynomial.
    – Lord Shark the Unknown
    Dec 29 '18 at 10:24










  • any more such ?
    – user629353
    Dec 29 '18 at 10:26










  • See also, the concept of the zero vector, which gives rise to similar questions.
    – Devashish Kaushik
    Dec 29 '18 at 10:42






  • 2




    Why the focus on this polynomial? One could also ask "what is the need of the X+1 polynomial?"
    – Did
    Dec 29 '18 at 10:44








  • 1




    @DevashishKaushik Have you had the curiosity to hover your mouse over the downvote arrow and to read what the popup attached to it says? Does the present question strike you as showing admirable research? (To prevent misunderstandings, I did not downvote and I very muchI resent having to say so because of your comment.)
    – Did
    Dec 29 '18 at 10:48
















-2














Someday while reading about polynomials (from: https://en.m.wikipedia.org/wiki/Polynomial), i came across with a topic, zero polynomial. It writes as:




enter image description here




My question: what is the need to introduce zero polynomial in mathematics?










share|cite|improve this question















closed as off-topic by Did, Cesareo, Martín Vacas Vignolo, Eevee Trainer, Leucippus Dec 31 '18 at 2:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Did, Cesareo, Martín Vacas Vignolo, Eevee Trainer, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.









  • 6




    When I add two polynomials, I like to get a polynomial.
    – Lord Shark the Unknown
    Dec 29 '18 at 10:24










  • any more such ?
    – user629353
    Dec 29 '18 at 10:26










  • See also, the concept of the zero vector, which gives rise to similar questions.
    – Devashish Kaushik
    Dec 29 '18 at 10:42






  • 2




    Why the focus on this polynomial? One could also ask "what is the need of the X+1 polynomial?"
    – Did
    Dec 29 '18 at 10:44








  • 1




    @DevashishKaushik Have you had the curiosity to hover your mouse over the downvote arrow and to read what the popup attached to it says? Does the present question strike you as showing admirable research? (To prevent misunderstandings, I did not downvote and I very muchI resent having to say so because of your comment.)
    – Did
    Dec 29 '18 at 10:48














-2












-2








-2







Someday while reading about polynomials (from: https://en.m.wikipedia.org/wiki/Polynomial), i came across with a topic, zero polynomial. It writes as:




enter image description here




My question: what is the need to introduce zero polynomial in mathematics?










share|cite|improve this question















Someday while reading about polynomials (from: https://en.m.wikipedia.org/wiki/Polynomial), i came across with a topic, zero polynomial. It writes as:




enter image description here




My question: what is the need to introduce zero polynomial in mathematics?







polynomials






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share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited yesterday







user629353

















asked Dec 29 '18 at 10:23









user629353user629353

1047




1047




closed as off-topic by Did, Cesareo, Martín Vacas Vignolo, Eevee Trainer, Leucippus Dec 31 '18 at 2:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Did, Cesareo, Martín Vacas Vignolo, Eevee Trainer, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Did, Cesareo, Martín Vacas Vignolo, Eevee Trainer, Leucippus Dec 31 '18 at 2:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Did, Cesareo, Martín Vacas Vignolo, Eevee Trainer, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.








  • 6




    When I add two polynomials, I like to get a polynomial.
    – Lord Shark the Unknown
    Dec 29 '18 at 10:24










  • any more such ?
    – user629353
    Dec 29 '18 at 10:26










  • See also, the concept of the zero vector, which gives rise to similar questions.
    – Devashish Kaushik
    Dec 29 '18 at 10:42






  • 2




    Why the focus on this polynomial? One could also ask "what is the need of the X+1 polynomial?"
    – Did
    Dec 29 '18 at 10:44








  • 1




    @DevashishKaushik Have you had the curiosity to hover your mouse over the downvote arrow and to read what the popup attached to it says? Does the present question strike you as showing admirable research? (To prevent misunderstandings, I did not downvote and I very muchI resent having to say so because of your comment.)
    – Did
    Dec 29 '18 at 10:48














  • 6




    When I add two polynomials, I like to get a polynomial.
    – Lord Shark the Unknown
    Dec 29 '18 at 10:24










  • any more such ?
    – user629353
    Dec 29 '18 at 10:26










  • See also, the concept of the zero vector, which gives rise to similar questions.
    – Devashish Kaushik
    Dec 29 '18 at 10:42






  • 2




    Why the focus on this polynomial? One could also ask "what is the need of the X+1 polynomial?"
    – Did
    Dec 29 '18 at 10:44








  • 1




    @DevashishKaushik Have you had the curiosity to hover your mouse over the downvote arrow and to read what the popup attached to it says? Does the present question strike you as showing admirable research? (To prevent misunderstandings, I did not downvote and I very muchI resent having to say so because of your comment.)
    – Did
    Dec 29 '18 at 10:48








6




6




When I add two polynomials, I like to get a polynomial.
– Lord Shark the Unknown
Dec 29 '18 at 10:24




When I add two polynomials, I like to get a polynomial.
– Lord Shark the Unknown
Dec 29 '18 at 10:24












any more such ?
– user629353
Dec 29 '18 at 10:26




any more such ?
– user629353
Dec 29 '18 at 10:26












See also, the concept of the zero vector, which gives rise to similar questions.
– Devashish Kaushik
Dec 29 '18 at 10:42




See also, the concept of the zero vector, which gives rise to similar questions.
– Devashish Kaushik
Dec 29 '18 at 10:42




2




2




Why the focus on this polynomial? One could also ask "what is the need of the X+1 polynomial?"
– Did
Dec 29 '18 at 10:44






Why the focus on this polynomial? One could also ask "what is the need of the X+1 polynomial?"
– Did
Dec 29 '18 at 10:44






1




1




@DevashishKaushik Have you had the curiosity to hover your mouse over the downvote arrow and to read what the popup attached to it says? Does the present question strike you as showing admirable research? (To prevent misunderstandings, I did not downvote and I very muchI resent having to say so because of your comment.)
– Did
Dec 29 '18 at 10:48




@DevashishKaushik Have you had the curiosity to hover your mouse over the downvote arrow and to read what the popup attached to it says? Does the present question strike you as showing admirable research? (To prevent misunderstandings, I did not downvote and I very muchI resent having to say so because of your comment.)
– Did
Dec 29 '18 at 10:48










2 Answers
2






active

oldest

votes


















4














How is a polynomial defined?



A polynomial in a single indeterminate x can always be written (or rewritten) in the form



$$ a_n x^n + a_{n-1} x^{n-1}
+ a_{n-2} x^{n-2} dots + a_{1} x^{1} + a_{0} x^{0}$$

where $ a_0,a_1,a_2 dots a_n$ are constants and $ x$ is the indeterminate



Now what if all the cofficent are equal to $0$?






share|cite|improve this answer





















  • Thanks, it helps
    – user629353
    Jan 5 at 16:46



















3














It is nice to be able to perform familiar operations on polynomials e.g. addition and multiplication. For addition to behave nicely, it needs an additive identity which is the zero polynomial. Also, if we wanted to exclude it then we would need to specify that the coefficients could not all be zero so the definition would become more complicated.






share|cite|improve this answer






























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    4














    How is a polynomial defined?



    A polynomial in a single indeterminate x can always be written (or rewritten) in the form



    $$ a_n x^n + a_{n-1} x^{n-1}
    + a_{n-2} x^{n-2} dots + a_{1} x^{1} + a_{0} x^{0}$$

    where $ a_0,a_1,a_2 dots a_n$ are constants and $ x$ is the indeterminate



    Now what if all the cofficent are equal to $0$?






    share|cite|improve this answer





















    • Thanks, it helps
      – user629353
      Jan 5 at 16:46
















    4














    How is a polynomial defined?



    A polynomial in a single indeterminate x can always be written (or rewritten) in the form



    $$ a_n x^n + a_{n-1} x^{n-1}
    + a_{n-2} x^{n-2} dots + a_{1} x^{1} + a_{0} x^{0}$$

    where $ a_0,a_1,a_2 dots a_n$ are constants and $ x$ is the indeterminate



    Now what if all the cofficent are equal to $0$?






    share|cite|improve this answer





















    • Thanks, it helps
      – user629353
      Jan 5 at 16:46














    4












    4








    4






    How is a polynomial defined?



    A polynomial in a single indeterminate x can always be written (or rewritten) in the form



    $$ a_n x^n + a_{n-1} x^{n-1}
    + a_{n-2} x^{n-2} dots + a_{1} x^{1} + a_{0} x^{0}$$

    where $ a_0,a_1,a_2 dots a_n$ are constants and $ x$ is the indeterminate



    Now what if all the cofficent are equal to $0$?






    share|cite|improve this answer












    How is a polynomial defined?



    A polynomial in a single indeterminate x can always be written (or rewritten) in the form



    $$ a_n x^n + a_{n-1} x^{n-1}
    + a_{n-2} x^{n-2} dots + a_{1} x^{1} + a_{0} x^{0}$$

    where $ a_0,a_1,a_2 dots a_n$ are constants and $ x$ is the indeterminate



    Now what if all the cofficent are equal to $0$?







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Dec 29 '18 at 10:38









    Rakesh BhattRakesh Bhatt

    1,015114




    1,015114












    • Thanks, it helps
      – user629353
      Jan 5 at 16:46


















    • Thanks, it helps
      – user629353
      Jan 5 at 16:46
















    Thanks, it helps
    – user629353
    Jan 5 at 16:46




    Thanks, it helps
    – user629353
    Jan 5 at 16:46











    3














    It is nice to be able to perform familiar operations on polynomials e.g. addition and multiplication. For addition to behave nicely, it needs an additive identity which is the zero polynomial. Also, if we wanted to exclude it then we would need to specify that the coefficients could not all be zero so the definition would become more complicated.






    share|cite|improve this answer




























      3














      It is nice to be able to perform familiar operations on polynomials e.g. addition and multiplication. For addition to behave nicely, it needs an additive identity which is the zero polynomial. Also, if we wanted to exclude it then we would need to specify that the coefficients could not all be zero so the definition would become more complicated.






      share|cite|improve this answer


























        3












        3








        3






        It is nice to be able to perform familiar operations on polynomials e.g. addition and multiplication. For addition to behave nicely, it needs an additive identity which is the zero polynomial. Also, if we wanted to exclude it then we would need to specify that the coefficients could not all be zero so the definition would become more complicated.






        share|cite|improve this answer














        It is nice to be able to perform familiar operations on polynomials e.g. addition and multiplication. For addition to behave nicely, it needs an additive identity which is the zero polynomial. Also, if we wanted to exclude it then we would need to specify that the coefficients could not all be zero so the definition would become more complicated.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Dec 29 '18 at 15:47









        Bill Dubuque

        209k29190631




        209k29190631










        answered Dec 29 '18 at 10:40









        badjohnbadjohn

        4,2421620




        4,2421620















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