Talk:Factorization

message: In my opinion, this section is a special case of a^2 -  b^2 being  a^2 - 2 b^2, which yields  (a-\sqrt2 b)(a+\sqrt2b) for one, and there is no way of doing this without radicals (assuming a and b are integers) like the editor asks for.
Furthermore, it is stated as if the editor wanted help in his homework, but of course without knowing the editor, I will not pass judgement on his intentions, just that it sounds terrible in the article. In any case, unless the section is relevant, which does not seem so, it should be deleted, or at least until what is proposed is found.
--GabKBel (talk) 03:35, 5 July 2011 (UTC)
thread_title: Factoring <math>a^2 - 2 b^2</math>

message: ===Table method (for quadratics)===
A less used (hard to teach, easy to learn) method often involves creating a multiplication table.
For example, let's work with 6x2 - 17x + 12.
Multiply first and last terms. (72x2)
What multiplies into 72 (first term) and adds up to -17(x) (middle term)?
-9 and -8
In the table, place the first term in the first box and the last in the last box. Fit the (in this example) -9 and -8 in the remaining boxes. Find the GCF up and down and side to side for each row for the answer.
6x2	-8x
-9x	12
The answer would be (3x-4)(2x-3)
This method is very decisive and much faster than the others. However, there are a few special rules surrounding the method, but when all of the rules are followed, it works every time.
:I am not sure this method is faster than the generalized AC method shown. In this example ac = 72. Examination of the factors of 72 gives -9 -8 = -17 = b, as above. From here we get:
:6x2 - 17x + 12 = (6x - 8)(6x - 9)/6 = (2)(3x - 4)(3)(2x - 3)/6 = (3x - 4)(2x - 3).  —Preceding unsigned comment added by 150.176.192.118 (talk) 15:51, 11 January 2011 (UTC)
thread_title:  Must be worked on (anyone know what the "special rules" are ?): 

message: A less used (hard to teach, easy to learn) method often involves creating a multiplication table.
For example, let's work with 6x2 - 17x + 12.
Multiply first and last terms. (72x2)
What multiplies into 72 (first term) and adds up to -17(x) (middle term)?
-9 and -8
In the table, place the first term in the first box and the last in the last box. Fit the (in this example) -9 and -8 in the remaining boxes. Find the GCF up and down and side to side for each row for the answer.
6x2	-8x
-9x	12
The answer would be (3x-4)(2x-3)
This method is very decisive and much faster than the others. However, there are a few special rules surrounding the method, but when all of the rules are followed, it works every time.
:I am not sure this method is faster than the generalized AC method shown. In this example ac = 72. Examination of the factors of 72 gives -9 -8 = -17 = b, as above. From here we get:
:6x2 - 17x + 12 = (6x - 8)(6x - 9)/6 = (2)(3x - 4)(3)(2x - 3)/6 = (3x - 4)(2x - 3).  —Preceding unsigned comment added by 150.176.192.118 (talk) 15:51, 11 January 2011 (UTC)
thread_title: Table method (for quadratics)

message: I would have expected that the prime factorisation of integers would be before factorisation of polynomials, etc. JPD (talk) 16:56, 7 August 2006 (UTC)
replies: text: Yes, you're right; that would be more logical.  I've changed it. —Mets501 (talk) 19:00, 7 August 2006 (UTC)
thread_title:  Order of sections 

message: a^n-b^n=c^2-d^2                                                                                                                                         
like 7^3-4^3=48^2-45^2                                                                   
Bhowmickr 07:15, 28 August 2006 (UTC)
replies: text: Not very exciting, since any odd integer may be expressed as a difference c^2-d^2, with both c and d being integers. JoergenB 12:55, 1 November 2007 (UTC)
replies: text: How does one express an integer of the form 4n+1 as a difference of squares of integers? that said, the difference in the original problem must either be 0 or -1 mod 4.  —Preceding unsigned comment added by 150.176.192.118 (talk) 16:07, 11 January 2011 (UTC)
replies: text: If a = 2n + 1, then a = (n + 1)2 − n2.—Emil J. 16:17, 11 January 2011 (UTC)
thread_title:  Difference of two cubes,forth powers,fifth powers,etc. 

message: A teacher at my schoool came up with this method. I like it.
You multiply (A)(C).
Use B. 
Find two numbers that multiply to give AC, and add to give B.
Let's say they are Z and Y
Now make two columns on paper...each with a ratio. A will be the first number in both ratios. 
Z will be the second number in the first ratio, and Y will be the second number in the second ratio.
Reduce if possible. Say you end up with A:Z and A:Y.
the answer will be (a+z)(a+y).
This is what they teach in grade 10. and it's easier/more convenient than the methods described here. 
 jmatt1122  CVU (Talk)  20:49, 4 November 2006 (UTC)
thread_title:  Ratio Method for factoring quadratics 

message: The article starts in a nice manner: integers, polynomials and matrices are considered.
Sections 1 & 2 still seem to preserve this.
Then, it goes in a quite wild way: Sections 3 - 6 are somehow "unclassified".
Then, section 7 pops up with logics, and matrices are present only in the "see also" section.
Who has ideas to re-equilibrate this a little?
As a first suggestion, could one make a 1- or 2-line summary for each of sect. 3-6
into the corresponding chapter (sect.1 or 2), make sect.3 on matrices
(or sect.3 : logics (since a little bit related to polynomial factoring), then sect.4: short summary on most important matrix decompositions).
I suggest to put details from sect.3-6 on (a) separate page(s).
Another idea would be a subsection of 2 with a title going somehow like "deterministic formulae and/or algorithms for speical cases".
(So one could know more easily what section would be useful for a given problem, e.g.)
Or, third idea, make some short sections at the beginning on "what the main body of this article not really is about: integer, matrix & logic factorization" with appropriate links, and then elaborate on the polynomial factoring methods (say, in increasing degree of the polynomials or some other order).
This is meant as a brainstorming - I'm missing better ideas, so please help. — MFH:Talk 22:08, 5 January 2007 (UTC)
thread_title:  Cleanup needed 

message: This article needs information on how to factor cubed polynomials and also why is it 7 imaginary rather than plus or minus y?
Gradster1 23:11, 8 May 2007 (UTC)
thread_title:  Cubed polynomials plus 7 imaginary 

message: I found a mistake in the fourth formula, it would be good if someone could review the formulas that come after this.AV-2 04:49, 3 September 2007 (UTC)
thread_title:  Error in "other common formulas" 

message: There is no reason that the factoring by grouping should use a trigonometry example. This unnecessarily excludes students unfamiliar with trigonometry from following the example.  Brentt (talk) 21:55, 24 June 2008 (UTC)
thread_title: Factoring by grouping

message: Am I the only one who thinks that this is of no value at all and that the entire purpose of that page is to promote their software? Anyone else thinks it should be removed? Almogo (talk) 15:18, 17 August 2009 (UTC)
thread_title: Last link in the external links section

message: In the introduction part of the article, the following is stated:
"
However, factors are not needed to divide evenly because they are still divisible by any number. For example, technically 3 and 8/3 are factors of 8. But, when factoring for tests teachers are looking for the even divisibility of the numbers.''
"
This seems to be written with certain math tests in mind, and I don't think it is relevant for the article as a whole. Any objections to deleting that part?
Trolle3000 (talk) 23:19, 3 October 2009 (UTC)
replies: text: The sentence is misleading and completely misguided. In the ring of integers, 3 does not divide 8, period. In the ring of rationals, 3 and 8/3 are true factors of 8, not just "technically". What particular teachers are looking for in particular tests is irrelevant. — Emil J. 10:52, 5 October 2009 (UTC)
thread_title:  Funny introduction to the article 

message: At least the talk page does; lots of old requests or concerns on this page seem to be unattended.
Also I added the factor theorem. I was surprised to find it missing in the other section (along with some recently added content that doesn't seem to make any sense... --Xali (talk) 23:54, 17 October 2009 (UTC)
thread_title:  I think this page requires clean-up and/or attention

message: The two are equivalent, though I would like to know where/when each term was popular. 18.111.42.150 (talk) 19:34, 15 August 2010 (UTC)
replies: text: The two are not equivalent. For example, 7 · 11 · 13 is the prime factorization of 1001, whereas 7 (as well as 11 or 13) is a prime factor of 1001.—Emil J. 12:39, 16 August 2010 (UTC)
thread_title:  Discuss the usage difference between "factor" and "factorization" 

message: Does it have a use? Fxm12 (talk) 23:48, 14 November 2011 (UTC)
replies: text: Yes, it does: the RSA is based on factorisation of large numbers is very slow. Hári Zalán (talk) 10:01, 6 March 2023 (UTC)
thread_title:  Does Factorization serve a practical purpose? 

message: Is there a way to export LaTeX Code from Wikipedia articles such as this? --Dagme (talk) 02:14, 1 May 2014 (UTC)
thread_title:  LaTeX Code? 

message: I have started a refactor of this page. The page, as originally envisioned (as I see it), was a gentle introduction to elementary factoring techniques. It was well done and was decently structured (but never completed). Over time, additions by various editors have disrupted the coherence of the article and introduced some subtle errors. In thinking about how to fix the page it became clear to me that the original organizing principle (doing a thorough job with quadratics in one variable and then move on to more complex polynomials) was too limiting for an encyclopedic article (it would be ok in a textbook). Thus, I am scrapping the original approach in reorganizing this page. I hope to keep the level of the article about the same and I will reuse all the quadratic stuff as examples. This will take a little time. Bill Cherowitzo  (talk) 18:50, 3 November 2014 (UTC)
thread_title:  Refactoring and adding references 

message: Substituted at 02:05, 5 May 2016 (UTC)
thread_title: Assessment comment

message: I know, for a long time that this is article was a mess (see the above thread). A recent edit by  showed me that it was full of mathematical errors an WP:OR opinions, mainly that a factorization must produce a simplification. Therefore I have rewritten the lead and the integer section, and started to rewrite the section on polynomials (not yet published). Doing that, I remarked another issue of this article: several hatnotes (there were too many) asserted that the article intends to be elementary. In fact, the simplest algebraic manipulations are detailed as if this were a first textbook for learning algebraic manipulations, and so many details are given that the main points become confusing. In the same time, the reader that is not supposed knowing simple algebraic manipulations is supposed to know what is a polynomial and what is the efficiency of a computation. Thinking about this, it appeared to me that the long section about factorization of polynomials was, in fact about factorization of expressions, as all methods apply when, for example, trigonometric functions are involved. 
For these reasons, I have started to rewrite the whole article, keeping it at least as elementary as it was, but placing it in the right mathematical context, and, when it is relevant, giving some insight toward more sophistical concepts. I hope that the result will be convenient for beginners, as well as for mathematicians. D.Lazard (talk) 14:44, 21 March 2018 (UTC)
replies: text: . The announced rewrite is now complete. D.Lazard (talk) 17:58, 26 March 2018 (UTC)
thread_title:  Rewriting this article 

message: A small remark from a non-expert: I am quite certain the Fermat number 2**32+1 is 4294967297 and not 4295967297 as mentioned in the text.
I think this is an error and should be corrected. [R.m.c. Ahn]  — Preceding unsigned comment added by 86.82.164.5 (talk) 23:21, 12 September 2018 (UTC)
replies: text: . Good catch. --Bill Cherowitzo  (talk) 03:55, 13 September 2018 (UTC)
thread_title: Error

message: Request to add "factorisation by inspection" to factorising polynomials section. This method uses abstracted concepts from factor theorum method, deserves its own section. Raakkk (talk) 01:39, 19 May 2023 (UTC)
replies: text: What size is it please 87.117.87.35 (talk) 18:31, 21 September 2023 (UTC)
replies: text: I  don't understand what size is ìt can you explain to the si 87.117.87.35 (talk) 18:33, 21 September 2023 (UTC)

text: A source is needed for including the method. I have never heard of a "factor theorum method". As far as I know, "factorization by inspection" cannot be very different from the content of section . If I am wrong, please, clarify your  meaning of "factorization by inspection". D.Lazard (talk) 20:42, 21 September 2023 (UTC)
thread_title:  Add Factorisation by inspection section to polynomial section