Here"s one excerpt from summary algebra book that I"m reading and my concern is provided later:

The difference in between a polynomial and also a polynomial function is mainly a distinction of viewpoint. Given$a(x)$ through coefficients in $F$: if $x$ is regarded simply as a placeholder, climate $a(x)$ is a polynomial;if $x$ is enabled to assume worths in $F$, then $a(x)$ is a polynomial function.

You are watching: What is the difference of the polynomials?

Then it goes:

Remember that two polynomials $a(x)$ and also $b(x)$ room equal iff corresponding coefficients space equal, whereastwo features $a(x)$ and also $b(x)$ room equal $a(x) = b(x)$ for every $x$ in their domain. These two notions the equality do not constantly coincide!

For example, think about the following two polynomials in $\wgc2010.orgbbZ_5$:$$a(x) = x^5 + 1$$

$$b(x) = x - 4$$

You may examine that $a(0) = b(0), a(1) = b(1), \ldots, a(4) = b(4)$, hence $a(x)$ and $b(x)$ space equal functionsfrom $\wgc2010.orgbbZ_5$ come $\wgc2010.orgbbZ_5$.

My question: can anyone call me why and also how $a(0)=b(0)$ for the over two functions?

abstract-algebra functions polynomials
re-publishing
point out
follow
inquiry Jun 23 "13 in ~ 12:46
user35885user35885
$\endgroup$
3
1
$\begingroup$
Lano I'm yes, really having hard times knowledge this book. The explanations room really vague. It's Pinter's "A publication of summary Algebra". I assumed it's the easiest publication in the market. $\endgroup$
–user35885
Jun 23 "13 in ~ 15:51
include a comment |

## 1 price 1

4
$\begingroup$
$a(0) = (0)^5 + 1 \equiv 1$ mode $5$.

$b(0) = (0) - 4 = -4 \equiv1$ mod $5$

Remember numbers in $\wgc2010.orgbbZ_5$ room the exact same if they different by a lot of of 5.

share
point out
monitor
answered Jun 23 "13 at 12:58

Eric AuldEric Auld
$\endgroup$
1
include a comment |

Thanks for contributing an answer to wgc2010.orgematics stack Exchange!

Please be sure to answer the question. Carry out details and also share her research!

But avoid

Asking because that help, clarification, or responding to various other answers.Making statements based upon opinion; back them increase with references or personal experience.

Use wgc2010.orgJax to layout equations. Wgc2010.orgJax reference.

To discover more, see our tips on writing great answers.

See more: King Taejo Of Goryeo Biography, Taejo Of Goryeo

Draft saved

send

### Post together a guest

surname
email Required, but never shown

### Post as a guest

surname
email

Required, but never shown

Featured on Meta
6
Why is it necessary that the evaluation map is a homomorphism?
4
Map native polynomial to polynomial function
1
Showing the a duty is a Vectorspace-Isomorphism?
associated
29
do we really need polynomials (In comparison to polynomial functions)?
5
Proof: two polynomials $P(x)$ and $Q(x)$ acquire same value for every $x \in \wgc2010.orgbb R$ if and also only if coefficients $p_i = q_i$ room equal because that every $i$
5
Polynomials vs polynomial features
2
exactly how are these two sentences equivalent?
1
Polynomial role and Polynomials.
2
Is there a relationship in between these polynomial concepts?
5
Is over there a polynomial i beg your pardon detects when the 2 smallest root of a given real polynomial room equal?
warm Network concerns much more hot concerns

concern feed

wgc2010.orgematics
agency
stack Exchange Network
site design / logo © 2021 ridge Exchange Inc; user contributions licensed under cc by-sa. Rev2021.10.15.40479

wgc2010.orgematics stack Exchange works ideal with JavaScript allowed