Let $f(x)= x^4 -10x^2+1.$   Using the rational root theorem, I see that the polynomial has no rational root. Therefore, it does not have any linear factor. If it's reducible over $\mathbb{Z},$ then it would a product of two irreducible quadratic polynomials.   I did this pathetic arithmetic, and then I have shown that the polynomial is in fact, irreducible over $\mathbb{Z},$ ie irreducible over $\mathbb{Q}$ by the Gauss's lemma.   Is there any better way to check that the polynomial is irreducible over $\mathbb{Q}$? Can we use Eisenstein Criterion by translating the polynomial? Any help/suggestions would be appreciated. Thanks so much.
How do I show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$? Someone says I should use the rational root test, but I don't exactly know how that applies. Thanks for any input.
Format string dynamically In some scenes in Avengers: Age of Ultron Iron man, War Machine, and Captain America try to lift Thor’s hammer but they end up failing. At some point Vision lifts it easily. How can Vision lift it? Sorting list based on values from another list 80's pop song with lyric "It's the story of my life if you wanna know" I'm trying to identify a song by a female 80's pop group.   Here are the lyrics I remember:     It's the story of my life if you want to know   a play where everything is meant to be   you're the story of my life and I can't let you go Read only field not working in page layout I have custom object called candidate. I have created field name called first name which is read-only in the page layout. Once a record is created with first name field populated I am able to edit that field. Why I am able to edit (I mean getting pencil icon). Can anyone suggest me for this issue? When I define amsthm theorem environments with shared counters, autoref messes up the names of the references. For example, in the output below, we should have "Definition 2" instead of "Theorem 2".  \documentclass{article}  \usepackage{amsthm} \usepackage{hyperref}  \theoremstyle{theorem} \newtheorem{theorem}{Theorem} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition}  \begin{document}  \begin{theorem} \label{wonderful-theorem} This is a wonderful theorem. \end{theorem}  \begin{definition} \label{awesome-definition} This is an awesome definition. \end{definition}  Look at the wonderful \autoref{wonderful-theorem} and the awesome \autoref{awesome-definition}.  \end{document} How do I uninstall Ubuntu Wubi? How does vampirism work? A PC in our group was off on his own following a recurring villain of our groups. He was paralyzed where he could move, and the vampire bit his neck. The vampire said "now you get to remain 19 (years old) forever" before he left the cave. This was all done in RP.  We found him later, and healed up his bite marks. Our characters know of vampires, specifically only the one that bit him (recurring villain), but don't really know how vampirism works, because it isn't a super common thing in this world yet.   My question as the player is:  How does RAW vampirism work in 5e?  Is it a disease that develops over time? Is it something where they have to die and be brought back as a vampire? Evaluating $\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$ for $x\in\mathbb{R}^{+}$ I am trying to evaluate the following sum. Here $x\in\mathbb{R^{+}}$. $$f(x)=\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$$ At present I do not know how to proceed. Any hints are appreciated. Thanks. "No root file system defined" error while installing ubuntu I am new to linux/ ubuntu and just downloaded the v11 of ubuntu to learn linux. I faced this "No root file system is defined" error while trying to install it. This is how I was proceeding -    Downloaded ubuntu v11 from the ubuntu.com website, wrote the iso into a bootable cd, and then got into the linux installation process on restarting; everything fine till here. In one of the screen during installation, there are three choices - install alongside windows, something else etc.. Since I have windows 7 in the C drive, I selected the first option - "Install alongside another OS".      Let me interrupt here to give my existing system details - HardDisk   size: 640GB.  Number of existing partitions - 5 C drive - label   windows - 160GB - has windows 7 installed D drive - label linux -   160GB - does not have any data E drive - label backup - 100GB - has   some data F drive - label entertainment - 100GB  - has some data G   drive - label work - 90GB  - has some data All of the above are in   NTFS format.    In the screen that follows, an image is shown with 2 parts and each part is shown to have size equal to 80GB. There is a horizontal slider in the middle of these two images, with which I can resize the partitions. The right side partition is labeled Linux. There is also an option to do 'advanced partitions'. On clicking advanced partitions on the above screen, a new screen is shown in which the partitions existing in my computer are shown - but the labels are different. I see that there are two partitions with size = 160GB each (as expected), and so I assumed that the first 160GB would be my existing C drive and the second on would be the partition which I had labeled as linux (drive D). So I selected the linux partition and clicked on proceed/ install now, and then this error was shown - "No root file system defined".. and I cannot proceed after this.   Please let me know two things here:   During the screen in point number 3 above, the image with slider was shown. Which partition (drive c: or d: or anyother) is being referred to here? Which one am I actually resizing - is it the existing c: drive which has windows 7 installed already, that is getting shrunk and then ubuntu getting installed in the remaining space? What does ""No root file system defined" error mean? How do I select the proper partition and continue with the installation?    P.S.:  I had already partitioned my drives as mentioned above, and the D drive with 160GB was specifically left free for installing ubuntu. I would like to Select D drive during setup and install ubuntu here, while still keeping the already installed windows7 in C drive.  Thanks! Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.   I was thinking of showing $A$ is not invertible, meaning it has an eigenvalue of $0$. Since no matter the power you give to $A$, it is still not the identity, you can deduce that at least one eigenvalue is indeed $0$. However this doesn't work if you have different eigenvalues in the Matrix, so I got stuck.  Help will be most appreciated. I want to better understand why the construction something + [adjective] makes grammatical sense. Background: I was recently reading a Washington Post article and came across the following sentence.  So if you fall in that category, [the movie] feels more like magic than repetitive.  (Note: I've copied the relevant spoiler-free sentence above; following the link to the article will open you up to movie spoilers! ) The phrase more like magic than repetitive struck me as odd, presumably because it was non-parallel (more like [noun] than [adjective]). I would have expected &quot;...more like magic than something repetitive.&quot; (Actually, that needs to be rewritten to flow better, but the point is that at least it appears to be grammatical.) Thus, one would have the noun phrase &quot;something repetitive,&quot; of the form &quot;[noun] [adjective].&quot; This got me to thinking about the use of adjectives after nouns. There is a great Stack Exchange article  that involves the characteristics of the adjective that indicate it should come after the noun. But I haven't been able to find examples of how the word &quot;something&quot; requires a postponed adjective. Consider the following sentences:  I want to buy something red. I am looking for something sweet to eat.  You cannot say:  *I want to buy red something. *I am looking for sweet something to eat.  But you can say:  I want to buy something (that is) red. I am looking for something (that is) sweet to eat.  So, my question:  Do the above examples mean that the &quot;something [adjective]&quot; construction is an example of the ellipsis of &quot;that is&quot;?  Is there something special about the word &quot;something&quot; that requires the postponed adjective? Note that I am NOT looking for details about adjectives that are postponed; I'm interested in the word that precedes the adjective (either &quot;something&quot; or similar words).   By the way, I am not interested in the following constructions, which are different:  I want to paint the house red. I tried to build the brick house taller.  Thanks in advance! Questions about right ideals What is a word that could define someone who likes to cause conflict? What would you call someone who does things knowing specifically that his/her actions will cause pain and/or conflict or completes an action just to get someone in trouble or hurt them?   For example, in  there are two people that are in love, but the Colonel goes out of his way to tell the father of the girl that the boy is a thief and would be bad for their reputation.   What is a word that would describe him? After installing Ubuntu Studio 12.04, I have found that it uses a low latency kernel.   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There could be a "View Question" button that pops up the question over the snippet editor and allows copying. Or maybe the Snippet Editor could be draggable and resizable, so you can reveal the question and copy from it; but this would require that it not be purely modal. How does iCloud Photo Library's "Optimize iPhone Storage" setting work in relation to other photo apps on iOS? If I have Optimize iPhone Storage enabled on my iPhone and my phone storage is completely full, I understand that iOS will only store a low-res thumbnail of many of my photos on the device. (The full high-res version of the image will only exist in iCloud and on devices with Download and Keep Originals enabled.)  But when only thumbnails exist on the device, how does that work in relation to other photo apps on iOS? For example, do third-party cloud-based photo apps (like Google Photos, Dropbox's Carousel, or Amazon Prime Photos) have access to the full high-res images from the iCloud Photo Library? 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