Talk:Factorization
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[edit] old comments
Whoa! Language alert!
- 15 factors into primes (verb)
- x2 - 4 factorises (verb)
- In mathematics, factorization (noun)
- The aim of factoring (noun)
Is there a good reason why there are two flavours of each? -- Tarquin 21:25 Sep 22, 2002 (UTC)
Unfortunately, both factor and factorize are used as synonymous verbs, each being more common in a different context, and each having its own noun form. When discussing the problem of breaking down large numbers, "factorize" is almost always used. In all other contexts it's usually "factor". I prefer the latter because it's shorter, but use the former when talking about the problem for large integers.
There's also the difference between using an "s" or a "z". That's purely a British vs. American issue, so it would be fine to standardize one way or the other on a given page.
I think there is a fast method of factoring integer into primes, but it requires a quantum computer.
[edit] Must be worked on (anyone know what the "special rules" are ?):
[edit] 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.
[edit] Sum/difference of two cubes
I'm here to learn, but shouldn't the factorization be (x-10)(x^2+10x+100) to expand to (x^3 - 1000)? Sparky 21:10, 15 April 2006 (UTC)
- You're so right. My apologies! --Mets501talk 21:31, 15 April 2006 (UTC)
- Haha no problem! Keep up the good work. Sparky 22:44, 15 April 2006 (UTC)
Also here is a problem: x^2-y^2+8y+4x-12 should I Factori "x^2-y^2" or "y^2+8y-12"first?
Factor it to
- x2 + 4x + 4 − (y2 − 8y + 16) = 12 + 4 − 16
- (x + 2)2 − (y − 4)2 = 0
—Mets501talk 15:14, 28 May 2006 (UTC)
FYI, I'm finding the description here very confusing. I've reread it several times. Is there a typo in the description of a^n - b^n and a^n + b^n - maybe left out an "even" in the wording? Anyway, the description is confusing.
[edit] Order of sections
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)
- Yes, you're right; that would be more logical. I've changed it. —Mets501 (talk) 19:00, 7 August 2006 (UTC)
[edit] difference of two cubes,forth powers,fifth powers,etc.
an − bn = c2 − d2 like 73 − 43 = 482 − 452 Bhowmickr 07:15, 28 August 2006 (UTC)
- Not very exciting, since any odd integer may be expressed as a difference c2 − d2, with both c and d being integers. JoergenB 12:55, 1 November 2007 (UTC)
[edit] Ratio Method for factoring quadratics
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)
[edit] cleanup needed
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)
[edit] Cubed polynomials plus 7 imaginary
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)
[edit] Error in "other common formulas"
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)
