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:

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

edited yesterday

asked Dec 29 '18 at 10:23

user629353

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.

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

|
show 2 more comments

-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:

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

edited yesterday

asked Dec 29 '18 at 10:23

user629353

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.

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

|
show 2 more comments

-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:

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

edited yesterday

asked Dec 29 '18 at 10:23

user629353

1047

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

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

polynomials

edited yesterday

asked Dec 29 '18 at 10:23

user629353

1047

edited yesterday

asked Dec 29 '18 at 10:23

user629353

1047

edited yesterday

asked Dec 29 '18 at 10:23

user629353

1047

asked Dec 29 '18 at 10:23

user629353

1047

asked Dec 29 '18 at 10:23

user629353

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

|
show 2 more comments

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

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

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

@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

|
show 2 more comments

2 Answers
2

active

oldest

votes

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 $0$?

answered Dec 29 '18 at 10:38

Rakesh Bhatt

1,015114

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

add a comment |

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.

edited Dec 29 '18 at 15:47

Bill Dubuque

209k29190631

answered Dec 29 '18 at 10:40

badjohn

4,2421620

add a comment |

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

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 $0$?

answered Dec 29 '18 at 10:38

Rakesh Bhatt

1,015114

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

add a comment |

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 $0$?

answered Dec 29 '18 at 10:38

Rakesh Bhatt

1,015114

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

add a comment |

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 $0$?

answered Dec 29 '18 at 10:38

Rakesh Bhatt

1,015114

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 $0$?

answered Dec 29 '18 at 10:38

Rakesh Bhatt

1,015114

answered Dec 29 '18 at 10:38

Rakesh Bhatt

1,015114

answered Dec 29 '18 at 10:38

Rakesh Bhatt

1,015114

answered Dec 29 '18 at 10:38

Rakesh Bhatt

1,015114

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

add a comment |

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

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

add a comment |

edited Dec 29 '18 at 15:47

Bill Dubuque

209k29190631

answered Dec 29 '18 at 10:40

badjohn

4,2421620

add a comment |

edited Dec 29 '18 at 15:47

Bill Dubuque

209k29190631

answered Dec 29 '18 at 10:40

badjohn

4,2421620

add a comment |

edited Dec 29 '18 at 15:47

Bill Dubuque

209k29190631

answered Dec 29 '18 at 10:40

badjohn

4,2421620

edited Dec 29 '18 at 15:47

Bill Dubuque

209k29190631

answered Dec 29 '18 at 10:40

badjohn

4,2421620

edited Dec 29 '18 at 15:47

Bill Dubuque

209k29190631

edited Dec 29 '18 at 15:47

Bill Dubuque

209k29190631

edited Dec 29 '18 at 15:47

Bill Dubuque

209k29190631

answered Dec 29 '18 at 10:40

badjohn

4,2421620

answered Dec 29 '18 at 10:40

badjohn

4,2421620

answered Dec 29 '18 at 10:40

badjohn

4,2421620

add a comment |

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