In this exercise I've shown first that if we have $P'(X)=0$ then the $Car K$ different $ 0$. Now they are specifing that if$ K$ is a finite field than $P$ is reductible. I've been searching for hours, tried to write the derivative of $P$ but I get nothing intersting.  Any Hint ?   Thanks for reading,
I'm hoping someone can give me a nudge in the right direction...     Let $F$ be a finite field, and let $f(x)$ be a nonconstant polynomial whose derivative is the zero polynomial.  Prove that $f$ cannot be irreducible over $F$.   I've got that every root of $f$ is a multiple root and that for $F=\mathbb{F}_{p^r}$, the exponent of every term of $f$ is a multiple of $p$.
Problem:  Ajax suggest-search on [n] ingredients in recipes. That is: match recipes against multiple ingredients.  For instance: SELECT Recipes using "flower", "salt" would produce: "Pizza", "Bread", "Saltwater" and so forth.  Tables:  Ingredients [     IngredientsID INT [PK],     IngredientsName VARCHAR ]  Recipes [     RecipesID INT [PK],     RecipesName VARCHAR ]  IngredientsRecipes [     IngredientsRecipesID INT [PK],     IngredientsID INT,     RecipesID INT ]   Query:  SELECT     Recipes.RecipesID,     Recipes.RecipesName,     Ingredients.IngredientsID,     Ingredients.IngredientsName FROM     IngredientsRecipes      INNER JOIN Ingredients     ON IngredientsRecipes.IngredientsID = Ingredients.IngredientsID      INNER JOIN Recipes     ON IngredientsRecipes.RecipesID = Recipes.RecipesID WHERE     Ingredients.IngredientsName IN ('salt', 'water', 'flower')   I am currently constructing my query using ASP.NET C# because of the dynamic nature of the WHERE clause.  I bites that I have to construct the query in my code-layer instead of using a stored procedure/pure SQL, which in theory should be much faster.  Have you guys got any thoughts on how I would move all of the logic from my code-layer to pure SQL, or at least how I can optimize the performance of what I'm doing?  I am thinking along the lines of temporary tables:  Step one: SELECT IngredientsID FROM Ingredients and INSERT INTO temp-table  Step two: SELECT RecipesName FROM Recipes joined with IngredientsRecipes joined with temp-table.IngredientsID Let K={(1),(12)(34),(13)(24),(14)(23)} show that K is a normal subgroup of the alternating group of degree A4 and find all the members of A4/K and write down the group table for A4/K.   i know that K is the Klein four group and i have already proven it is a normal subgroup but i need a start on approaching the A4/K part of this question no direct answers are necessary,just ideas thank you! :) Is it possible for an American to get a Chinese visa in Hong Kong? Why does locking the rear tires on a vehicle cause it to spin? are often used in motor-sports and stunt driving to turn around tight corners.  Essentially, the driver applies the handbrake as he enters the turn, in order to "kick out" the back end and slide the vehicle around the corner.  However, applying the handbrake hard enough to lock the rear wheels while traveling straight will cause the rear of the vehicle to "kick out".  Given enough speed, the vehicle will spin 180 degrees.  Why do sliding wheels on a car want to "get in front" of rolling wheels? Is there any adjustment required when computing the correlation coefficient between:   continuous and discrete variable  two discrete variables ?    Thanks ! facing difficulty to create dynamic xpath for City field of UTest website I am beginner in automation field, I am trying to automated one of the module, I have tried many different XPATH to fetch proper XPATH for City field o UTest site. Im trying to automate registration module as one of my assignment. I have tried my different xpath example below:  //xpath="//body/div[@class='pac-container pac-logo']/div/span[2]/span" //div[@class='pac-item']/span[3] //div[@class='pac-item']/span //div[@class='pac-container pac-logo']/div/span[2]/../span[3]   the following code written:  //xpath to send data in field @FindBy(xpath="//input[@placeholder='Enter a location']") WebElement city;  //xpath for list to appear @FindBy(xpath="div[@class='pac-item']/span") List&lt;WebElement&gt; City;  public void EnterSignupTwo(String CiTy) throws Exception {     city.clear();     city.sendKeys(CiTy);     Thread.sleep(3000);     System.out.println("the size of List " +City.size());//printing list size      for(int i=0; i&lt;City.size(); i++ ) {         String cities = City.get(i).getText(); //storing list element in String         System.out.println("Converted value of city :"+cities); //print of total list      if(cities.contains(CiTy)) //if parameterized match with Available then click     {         System.out.println("enter specific value of city :"+City.get(i).getText());         City.get(i).click();         break;     } }   kindly refer the In the current era of cricket, we see batsmen using switch hits to play a ball. That is, while playing a ball they change their batting side (left to right handed and vice versa) just before the ball comes to them.  My question is, can a bowler bowl a switch ball? Meaning, can a left hand bowler bowl right handed to a batsman? If it is not permitted, then is it not unfair to the bowlers that batsmen can change their batting style but not the bowlers? Or are there are any rules against a switch hit? Volumetric Lighting is not working I have a simple setup to try out Volumetric Lighting. I have a spot lamp and Volume Scatter set for the World. The cube has a window for the light of the spot lamp.     But no Volumetric Lighting. I have read most questions on this subject. But I have no idea where I am going wrong. I would like to use client-side Javascript to perform a DNS lookup (hostname to IP address) as seen from the client's computer. Is that possible? My question is simple, why do we believe  to be absurd? Is the Ultra-violet catastrophe incorrect or is it only because we can not create or know of a perfect emitter? I am a bit confused as to why Quanta was necessary. I accidentally closed it without voting, how can I find it? When I suggest declaring war on the target it says there's already a proposition to do so. Is "princessship" a real word? Are there any other words which have the same letter 3 times consecutively? Notation problem in integration: write $dx$ or ${\mathrm{d}}x$? How to read a single character from the user? Is there a way of reading one single character from the user input? For instance, they press one key at the terminal and it is returned (sort of like getch()). I know there's a function in Windows for it, but I'd like something that is cross-platform. I am having trouble getting onto a server in Minecraft PE on iOS. When I tap on the person's server it just says invalid name:    I have tried turning off and restarting the iPad, going to home screen and logging back into the server but I have had no luck and no change. Is there a reason why this is so? Link2SD not working completely My Link2SD doesn't seem to be fully working. I noticed this when updating the Facebook application. Google Play prompted me of insufficient storage. I first uninstalled some apps but I got curious so I checked Link2SD's storage info, I got this:   (Click image to enlarge)  As you can see, the internal storage only has mere 70mb left. What's peculiar is, these are the only apps I have NOT linked:   (Click image to enlarge)  I tried moving one linked app (Amazing Alex) to the sd card (normal Android way) and sure enough, the free space on my internal storage got bigger by about an additional 20mb-ish.  Why is this happening? Why isn't Link2SD moving the data to my sdext2? How do I solve it? Why do we use the object instead of the subject pronoun in constructions like "stupid me"? I'm trying to find out how come we say lucky me and stupid us rather than lucky I and stupid we. My understanding is that this is not a recent invention, but a relic from the distant past where it was a dative construction. However, I don't see the reason for using any case other than the nominative in this construction to begin with.        He went surfing. → Lucky him went surfing.   I got pulled over. → Stupid me got pulled over.   They bought a house. → Thoughtless them bought a house.      This is rather intriguing. After thinking about it for a while, I couldn't come up with any other language, Germanic or otherwise, where simply introducing an adjective would dictate a change of grammatical case. This appears to be an English peculiarity. How far can it be traced back? Can anyone comment on its background? When should static_cast, dynamic_cast, const_cast and reinterpret_cast be used? Can an ideal in a commutative integral domain be its own square? If $I$ is a non-zero proper ideal of a commutative integral domain, is it possible for $I$ to be its own square? Can't quantum teleportation be superluminal some percentage of times? I apologize if this is a really silly question.   In the (textbook) quantum teleportation algorithm, in the step right after Alice has measured her system but before she has sent her classical information to Bob, she is about to send one of the following values: 00,01,10,11.   What if Bob doesn't want to wait and simply takes a guess? Wouldn't there then be superluminal communication 25% of the time?