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Question Number 188834 by sciencestudentW last updated on 07/Mar/23
does the multinomial name a polynomial?
$${does}\:{the}\:{multinomial}\:{name}\:{a}\:{polynomial}? \\ $$
Commented by mr W last updated on 07/Mar/23
poly∗ means multi∗.  poly is Greek. multi is Latin.
$${poly}\ast\:{means}\:{multi}\ast. \\ $$$${poly}\:{is}\:{Greek}.\:{multi}\:{is}\:{Latin}. \\ $$
Commented by sciencestudentW last updated on 07/Mar/23
i saw in some books that every  polynomial  is called a multinomial but every multinomial  isn′t called a polynomial .  what do you think about it?
$${i}\:{saw}\:{in}\:{some}\:{books}\:{that}\:{every}\:\:{polynomial} \\ $$$${is}\:{called}\:{a}\:{multinomial}\:{but}\:{every}\:{multinomial} \\ $$$${isn}'{t}\:{called}\:{a}\:{polynomial}\:. \\ $$$${what}\:{do}\:{you}\:{think}\:{about}\:{it}? \\ $$
Commented by mr W last updated on 07/Mar/23
Commented by Rasheed.Sindhi last updated on 08/Mar/23
In dictionary poly∗ & multi∗ have  same sense, no doubt!   But as a mathematical term they  may be defined in different way.  (though I′m not sure of that)  Perhaps the mentioned book has done this.  For example x+2+1/x is not a  polynomial but it maybe multinomial  in view of the book.
$${In}\:{dictionary}\:{poly}\ast\:\&\:{multi}\ast\:{have} \\ $$$${same}\:{sense},\:{no}\:{doubt}! \\ $$$$\:\mathcal{B}{ut}\:{as}\:{a}\:{mathematical}\:{term}\:{they} \\ $$$${may}\:{be}\:{defined}\:{in}\:{different}\:{way}. \\ $$$$\left({though}\:{I}'{m}\:{not}\:{sure}\:{of}\:{that}\right) \\ $$$${Perhaps}\:{the}\:{mentioned}\:{book}\:{has}\:{done}\:{this}. \\ $$$${For}\:{example}\:{x}+\mathrm{2}+\mathrm{1}/{x}\:{is}\:{not}\:{a} \\ $$$${polynomial}\:{but}\:{it}\:{maybe}\:{multinomial} \\ $$$${in}\:{view}\:{of}\:{the}\:{book}. \\ $$
Commented by sciencestudentW last updated on 08/Mar/23
thanks you are agreed with me that  every polynomial is called multinomial  but every multinomial isn′t called   polynomial ok?
$${thanks}\:{you}\:{are}\:{agreed}\:{with}\:{me}\:{that} \\ $$$${every}\:{polynomial}\:{is}\:{called}\:{multinomial} \\ $$$${but}\:{every}\:{multinomial}\:{isn}'{t}\:{called}\: \\ $$$${polynomial}\:{ok}? \\ $$
Commented by Rasheed.Sindhi last updated on 08/Mar/23
This depends upon how you define  multinomial. If multinomial means  only multiterm expression, then  yes: every polynomial is a multinomial  but every multinomial may not be  necessarily a polynomial.
$$\mathcal{T}{his}\:{depends}\:{upon}\:{how}\:{you}\:{define} \\ $$$${multinomial}.\:{If}\:{multinomial}\:{means} \\ $$$${only}\:{multiterm}\:{expression},\:{then} \\ $$$${yes}:\:{every}\:{polynomial}\:{is}\:{a}\:{multinomial} \\ $$$${but}\:{every}\:{multinomial}\:{may}\:{not}\:{be} \\ $$$${necessarily}\:{a}\:{polynomial}. \\ $$
Commented by mr W last updated on 08/Mar/23
i googled and found no generally  acknowledged definition for  “multinomial” in mathematics like  that for “polynomial”. so everybody  can understand what he likes.
$${i}\:{googled}\:{and}\:{found}\:{no}\:{generally} \\ $$$${acknowledged}\:{definition}\:{for} \\ $$$$“{multinomial}''\:{in}\:{mathematics}\:{like} \\ $$$${that}\:{for}\:“{polynomial}''.\:{so}\:{everybody} \\ $$$${can}\:{understand}\:{what}\:{he}\:{likes}. \\ $$
Commented by Rasheed.Sindhi last updated on 09/Mar/23
Thanks a lot sir!
$$\mathbb{T}\boldsymbol{\mathrm{han}}\Bbbk\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{lot}}\:\boldsymbol{\mathrm{sir}}! \\ $$

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