Wikipedia:Reference desk/Archives/Mathematics/2009 June 14

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June 14

alzebra quary of 9 standard

question  : x⁴+1+x² —Preceding unsigned comment added by V neeta (talk • contribs) 01:00, 14 June 2009 (UTC)

That's not a question, it's a context-free string of symbols. What do you want us to do with them? Algebraist 01:23, 14 June 2009 (UTC)

The fact that this question is in the context of 9th grade algebra and that he has not explicitly given the question suggests that the OP wants us to simplify the given algebraic expression. However, it is somewhat clear that the expression cannot be simplified further, unless of course you consider factoring x² from x⁴ + x² to be a "simplification." In this case, therefore, the question appears to be a "trick question" in that no simplification is possible, although in the given context of questions, an algebraic expression in any other question could be simplified. Of course, I may have interpreted the question completely incorrectly. --PST 04:21, 14 June 2009 (UTC)

The polynomial can be viewed as a difference of squares, namely (x⁴ + 2x² + 1) − x², leading to the factorization (x² − x + 1)(x² + x + 1). This may be useful as an intermediate step on the way to the roots, if that's what the OP wants. Michael Slone (talk) 04:55, 14 June 2009 (UTC)

Or it could be that he wants to solve the equation x⁴ + 1 + x² = 0. In that case, I'd start with u = x², solve the quadratic equation in u, and then solve the two separate quadratic equations in x. Alternatively, solving the two quadratic equations in x suggested by Michael Slone's posting would give the same result.

Probably a textbook said something like "Factor the following polynomials", then had a numbered list of problems, and somewhere among them there appeared x⁴ + 1 + x². Then the poster neglected the words written at the top and posted only the polynomial. The words are where the actual question was. The poster failed to realize that. In other words, the poster had no question about mathematics, but was unsuccessfully attempting to transmit the textbook's question to us.

Just a guess.

That such absurd lunatic behavior is routine shows one aspect of what's wrong with pretending to require people to learn math when they don't want to do so and spend the whole course kicking and screaming. Michael Hardy (talk) 16:09, 14 June 2009 (UTC)

I don't completely agree; I think in most cases it is just a problem of lack of correct mathematical language, and sometimes, just a problem of English for non-native speakers (I suspect the present case could be one). In fact, while the "Assume good faith" guideline is generally followed, I fear we can't say the same of "Assume no total stupidity" (even between answers, sometimes!). For instance, we often see people asking for "solution of a polynomial", which is a nonsense taken literally, yet we don't need to presume idiocy. Sometimes in these cases we eventually see that the questioner did know what he said and even understood the answer. Here, as PST points out, the context of 9th grade algebra makes it clear that the request is a factorization. If a person of mean intelligence has only seen polynomials as objects to be factorized, he may well assume that it is implicitly understood that you can't do other, and that the meaning of an polynomial be "factorize me", as "3 x 2" means "multiply 3 by 2". To make an example, if someone offers me a banana, I am authomatically lead to take and eat it, and I don't even wonder if he may mean I should put it in my ears.

Note the approach by Algebraist: just a short answer: your question is not properly formulated / please restate your question. This way the poster will not be intimidated, and we can also understand better the situation. The subsequent defence of the questioner by PST was maybe not necessary --possibly refrained a bit the reply. However, I do not have solutions... maybe sometimes we should wait for the OP's reply, when he's been requested for clarifications. If we only could, the best would maybe something like in Brazil: as soon as somebody puts an unclear question, a group of Regulars implodes in his room, take him and in the case furnishes him with the needed mathematics. --pma (talk) 21:20, 14 June 2009 (UTC)

I agree with pma above. Although the OP may have phrased his question in an "incompetent style", one should be aware that this does not give an indication of his mathematical knowledge. On the other hand, it could well be the case that the OP knows English reasonably well but cannot use mathematical terminology appropriately. In this case, I still feel that we should not attack the OP because I am sure that most of us were at this stage at some point. In particular, when one first learns a concept, appropriately employing correct terminology is difficult for the average.

I guessed that the OP wanted a "simplification" of some sort, performed by adding/subtracting like terms. Usually, in my experience, I would expect such questions not to be given in the 9th grade for usually such students do not have a good understanding of algebra. I could be wrong, however.

On the other hand, the OP is probably not going to return to this help desk (and has probably not seen this discussion) so I do not really see much point in continuing. --PST 00:52, 15 June 2009 (UTC)

The comments of pma and Point-set topologist seem to make a certain amount of sense until I go back and look at what the original poster actually wrote. It's understandable that incorrectly used terminology appears on this page, but this poster used no terminology at all and behaved in the manner suggested by my guess. But maybe all sorts of weird people that I don't know about are out there.... Michael Hardy (talk) 22:51, 15 June 2009 (UTC)

well... not so weird after all: in the most efficient way, the OP got a number of very satisfactory answers --including yours, I suppose... ;-) pma (talk) 23:10, 18 June 2009 (UTC)

For the OP, now you've seen how that one was solved you can try factorizing x⁴+4 Dmcq (talk) 12:16, 15 June 2009 (UTC)