Division Definition and 486 Threads

Here's the problem I have to do: Let f(x)= x^3 -7x^2 +17x-15 One zero of f(x) is K=2-i find all others and write f(x) in a factored form. I ended up getting: f(x)= x^2 -x+2 Is this correct? Thanks

Homework Statement x^2-x-13/(x^2+7)(x-2) hello i am having trouble solving this problem.. could anyone please show me how to do this step by step? i know polynomial long division is required before it can be converted to partial fractions. I also know the answer is 2x+3/x^2+7 - 1/x-2...

Not sure when this problem in my book says to calculate by long division the series 1/(1+x) = 1 - x + x^2 - x^3 + ..., and then integrating termwise between 0 and x. I am really rusty on these types of problems and need help understanding how to even begin T.T. Thanks for the help.

I'm trying to list the cosets of the following ring and describe the relations that hold between these cosets. R=Z_4[x]/((x^2+1)*Z_4[x]) I'm using the division algorithm since x^2+1 is monic in the ring Z_4[x].Now for every f that belongs to Z_4[x] by the division algorithm...

I am trying to solve the following problem: $$(\sqrt{x} + \delta)/x$$ Using long division, I get: $$\sqrt{x}$$ On top and I end up with $$-\delta\sqrt{x}$$ On the bottom and am unsure how to proceed from there? I'm sorry I can't write out all my work out as I'm not sure how I could...

What is the difference between lower division linear algebra and upper division linear algebra?

"Weirdness" of polynomial long division algorithm Hello. So, i just started to learn about the polynomial long division. As an introductory example, the book presents the long division of natural numbers, claiming that its basically the same thing. The example: 8096:23 Solution...

Hey guys, I'm an electrical engineering student with a strong interest in physics. I would like to work through classical mechanics, E&M, and thermodynamics books. I'm not sure if there's another subject that is usually covered in classical physics (perhaps waves/optics?) but if so, I'd like...

Hi. i wonder how come one doesn't divide with (n-1) when finding the sample mean variance. Homework Equations Shouldn't I divide with n -1 since it is samples i am dealing with? The Attempt at a Solution I don't really have any idea as to why the book uses n. I have googled but...

Homework Statement The problem is about solving the homogenous differential equation (x2 + y2)dx + (x2 - xy)dy = 0 using substitution, in this case y=ux. This is the example they go through in the textbook (A First Course in Differentia Equations with Modeling Applications, 9th Edition, Zill...

Homework Statement On the morning of September 30, 1982 the won lost records of the three leading baseball teams in the Western Division of the National league were: Braves Won: 87 Lost:72 Giants Won: 86 Lost: 73 Dodgers Won: 86 Lost: 73 Each team had 3 games...

Homework Statement \frac{x^3+x^2-5x+3}{x^3-3x+2} Homework Equations The Attempt at a Solution well I'm drawing that long division house with x^3-3x+2 on the outside and x^3+x^2-5x+3 on the inside. I'm seeing that x^3 goes into x^3 one time, so i put a 1 on top of the...

Homework Statement Show that, for positive integers a and b, there exists unique integers q and r such that a = bq + r and -b/2 < r \leq b/2. Homework Equations We can assume the standard division algorithm holds. That is, for integers a and b, there exists unique integers q and r such...

if f(x)modg(x) is valid(means , if it yield a remainder) then , can there be negative powers of x in f(x)? for example is (x-29)mod(x2 - 3) possible ? can we do modulo division like this or is it strictly defined only for positive powers of x?

Homework Statement Prove that for every integer n, 15|n iff 5|n and 3|n. I have proven the "if" direction. My question regards the "only if" portion of the proof. So far I have: (<--) Suppose 5|n and 3|n. Then there are j,k ∈ Z for which n = 5j and n = 3k. *above, Z stands for...

This question seems to befall everyone at one point or another. So much so I begin to get deliberately silly when it is asked http://www.wolframalpha.com/input/?i=Abs%5B1%2F0%5D Anyway, I'm wondering if there is a sticky present on these forums that addresses it specifically. Something...

Homework Statement Apply the division algorithm for polynomials to find the quotient and remainder when (x^4)-(2x^3)+(x^2)-x+1 is divided by (2x^2)+x+1 in Z7. Homework Equations The Attempt at a Solution I worked the problem and got that the quotient was (4x^2)-3x-1 and the...

Homework Statement Express in terms of logarithms x, y, z or w. Problem: loga(x8w/y2z4) Homework Equations log(u/w) = log u - log w log(uw) = log u + log w The Attempt at a Solution Here are my attempts: As you can see, the answers are pretty similar. I'm assuming...

Within the next year, I'm transferring from the local community college to the state university to complete my BS in chemical engineering. Right now I have about 3.5 gpa in my lower division courses (math, chem, physics, intro engineering, etc). Obviously, I'm going to work as hard as I can to...

Hi, I was told by a physics tutor that if you do the following you will result in pi with a complementary between the heaviest quarks and leptons in forms of spin 0 and 1. So I copied what she was saying: ((Top Quark mass/Tau mass)/(Charm Quark mass/Muon mass)) / ((Charm Quark mass/Muon...

Hello there! I have a problem with conteptual understanding of the bandwith od channels that use frequency division multiplexing. How i understand that FDM works: We have a transmitter that transmits on one frequency f and the receiver that listens on that frequency. They can communicate...

I am taking a first course in algebra and I am having issues with a detail in this proof that every finite domain is a division ring. The argument that I used is that (because of cancellation in domains) left & right multiplication by a nonzero element r in a domain R gives a bijection from R...

As part of solving a DE I need to make this friendlier to integrate: \frac{2u}{1+u^{-2}} I figured trying to divide it couldn't hurt. I got: u^{-1}+u^{-3} I can't type out all the steps easily, I'm on a mobile device at the moment. That answer looks suspect, did I do it correctly?

Homework Statement (2) P is a prime number and a and b are positive integers . We Know... p | a^6 \ and p | a^3 + b^7. how do i find out how to prove that p | b? Homework Equations if a | b, then a | bx for every x in Z if a | b, and a | c, then a | bx + cy for any...

Prime Division HELP! Homework Statement I need to be able to understand and likely prove that for any positive odd integer n, 8 | (n^2 -1 ) Homework Equations The Attempt at a Solution odd can be said to be n = 2k +1 so 8 | (2k + 1)^2 -1

Hello, I can't understand where the '2' came from in this equation. 5x^2y / 10xy^3 = x/2y^2 I can see how the other values were calculated but the '2' before the y^2 is puzzling me. Thanks for any clarification.

I haven't been able to figure this out but I am sure it's very simple but I can't understand how to do it. If you take 5 x 0.5, that is the same as 0.5 + 0.5 +... Alright so how do you break a division problem down? I realize how dividing by a number greater than 1 works, but under 1 I...

Hi, I have seen a discussion similar to the question I am asking right now on the forum before, but I did not understand it and do not know if a conclusion was reached. In F = ma, F, or force net, is a vector and acceleration is a vector. When solving for m, or m = F/a, you are dividing...

show (n^2)! is divisible by (n!)^n+1 base case 1 divides 1 so I did the induction and got (n^2+2n)!=((n+1)^n * (n!) *(n!)^n+1 (n^2+2n)*...*(n^2)!=((n+1)^n * (n!) *(n!)^n+1 can we conclude that (n^2)! is divisible by (n!)^n+1 for all n from there because we have the bold...

Homework Statement Just tried something out and was wondering. If I have a vector X and do the division 1./X then that will result in a vector in which each element is the reciprocal of the corresponding element in X right? But what does 1/X do? I'm wondering because I noticed that the result...

Homework Statement (v-4)/(5v+1) The Attempt at a Solution I'm an engineering student, and I'm taking Differential Equations, but I can't remember how to do simple things like this. A walk through explanation would be very much appreciated, I don't have a lot of time to spare. The...

Homework Statement How to solve x for these inequality? Homework Equations |x-2|/|x+3|> (x+2) / (x+1) The Attempt at a Solution (x - 2)/(x + 3) > (x + 2) / ( x+1) the left side holds the condition that is x >= 2 however, I wonder the next step. should I crossly multiply so...

Homework Statement Q = rational numbers My professor proved that it is closed under addition yesterday. I kinda understood a bit... How the heck does it work for when n_1 or n_2 = 0?

Unphysical Division By Zero for Trivial Case of Zero Field Location Homework Statement Q1 and Q2 are two positive charges a distance s apart. Find the distance x from Q1 where the field is zero. Homework Equations E=\frac{kq}{r^2} The Attempt at a Solution Let's put Q1 at the...

So, I can see that it works by dividing a number by its base, recording the remainder, and then repeating until the answer is 0 (instead of a fraction, you wind up with an answer of 0 with a remainder). But how do I convert all the steps' answers&remainders into a binary number?

This is going to be kind of a long post, and I'm citing the author because it's directly from a textbook, but I'm assuming this proof is standard and I won't be doing anything unethical. I'm basically going to post it with my questions interrupting the text. I'm not sure how he got from some...

Homework Statement I'm trying to divide 1010 by 1001 Homework Equations The Attempt at a Solution So far all I have is _1___________ 1001 |1010.000000000 1001 ------ 0001 I know that 1001 divides into 0001 0 times, but I don't know...

Homework Statement Let p be a polynomial function with p(a)= 0 =p'(a) for some real a. Which of the following must be true? A) p(x) is divisible by x+a B) p(x) is divisible by x^2+a^2 C) p(x) is divisible by x^2-a^2 D) p(x) is divisible by x^2+2ax+a^2 E) p(x) is divisible by x^2-2ax+a^2...

What is division? 12 ones split up into 3 things is 4 ones (per thing.) 1 one split up into 100 things is 1/100 ones (per 1 thing.) Thus, "5 ones split up into 1/100 things is 500 ones (per 1 thing)" is probably better understood as "5 ones split up among hundredths of a thing is 500 hundredths...

I was self-studying Discrete Mathematics and I found the following problem. Homework Statement Show that whenever a and b are positive integers, then (2^a-1)\mod(2^b-1)=2^{a\mod b}-1 The attempt at a solution I don't know if there is a more rigorous way of solving it, but I came up with the...

Homework Statement I apologise that this is not in LaTeX, but i just couldn't find the codes Use long division or synthetic division: (9x^4 -x^2 - 6x+2) / (3x-1) The Attempt at a Solution So the root is x = 1/3 P(1/3) = 0, no remaindar 1/3 | 9 0 -1 -6 2 ...|...3 -1 0 -2 ___________...

Homework Statement Albinism in humans is controlled by a recessive allele. How many copies of this allele will be found at one of the poles of a cell at telophase I of meiosis in an albino person. A.23 B.4 C.2 D.1 Homework Equations The Attempt at a Solution Let rr be the recessive...

given (-1)! = \tilde{\infty} , which is complex infinity the real part of \tilde{\infty} is \overline{?} which is "a quantity whose magnitude cannot be determined" as stated in wolfram's site at http://functions.wolfram.com/Constants/ComplexInfinity/introductions/Symbols/ShowAll.html"...

Hi, I am looking for an explanation, if any, on why every integer square leaves remainder 0 or 1 on division by 4. Appreciate your time and help bluemoon2188

I just took a first semester of a first year physics course for scientists and engineers. Even though I thought that course work was rather rigorous, I did well and got an A in the course. I'm thinking about going into biophysics, but need to have a GPA in the range of 4.0-3.9 since I plan to...

I'm taking calculus for scientists and engineers and was wondering how much harder are upper division courses like partial differential equations, ordinary differential equations, and complex analysis than calculus?

Homework Statement Divide 2x5+x-1 by 3x2+1 in Q[x], Z5[x], and R[x] The Attempt at a Solution I believe the answer should be the same in Q[x] and R[x] and after division I got 2/3x3-2/9x with remainder 1 2/9x-1. I had trouble in Z5 and would like someone to help me. So far I...

Homework Statement This question was on a test in a math contest I was recently in, and I cannot seem to figure out how to get the answer: Let f(x)=x7+x6+x5+x4+x3+x2+x+1. If k is a positive integer such that 53 < k < 115, find the sum of all distinct k such that the numerical remainder...

Homework Statement Find the remainder of x^4 + 3x +2 after division by x+3 in Z5[x] Homework Equations my quotient after dividing was: x^3 + 2X^2 + 4x +1 The Attempt at a Solution I found the remainder to be 4. If anyone has time, I believe I made a mistake somewhere and would...

I'm struggling with how to even begin with this problem. Find the remainder of the division of 75!*130! by 211. 211 is prime, so I know the remainder is not 0. I'm not sure where to start though. Thanks!