Division Definition and 469 Threads

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...

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...

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 (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!

I'm not sure at all how best to approach this problem. Basically, the application is for practicing mental arithmetic. Most of the features are pretty easy, with the exception of division, which is the topic here. I accept a minimum and maximum for the first and last numbers in the division...

There must be about the same number of upper division classes for this engineering major as there are lower division? It would seem? Ok, so, this link shows lower division classes for the major, it does not show upper, so these are the classes for an engineering B.S. (In other words, these...

Homework Statement It's a physics problem, where i have to evaluate the root-mean-square radius defined by the expression below. (First for a constant \rho, then for a "(r)dependent" \rho).Homework Equations (\int{_0}{^\infty} \rho r^4 dr / \int{_0}{^\infty} \rho r^2 dr) ^(1/2)The Attempt at a...

Homework Statement see attached for circuit from your result from part b, use voltage division to find the voltage drop across the 2k ohm resistor. my result from b was 250V part b question was voltage drop across 10K resistor Homework Equations The Attempt at a Solution R_T=5k...

I have been doing some homework on synthetic division today. Most of it is pretty straight forward, until I got to a problem with complex number I was able to solve the first problem (x^3 – 3x^2 + x – 3) / (x-i) By using +i for the ‘synthetic divisor constant’ (sorry don’t know the proper...

Hi there! I have been reading Apostol's "Calculus: Volume 1" and have been trying to prove a few theorems using specific field axioms(note that this is not a "homework" question since I have not been assigned it, but instead, chosen to attempt it out of curiosity). Although I am not a math...

Is it zero divided by zero even a division? According to some, it is not, because division would have three requirements: 1) That any quotient must be a number. 2) That any quotient multiplied by a divisor must give us a dividend, which presupposes that any quotient is a number. 3) That no...

Can anyone please explain to me how and why do restoring and non restoring algorithms for division work and please provide me with a correct flowchart for the non restoring division.

Hi guys, I am designing an OFDM system and then upconverted at 1 GHz. Now I have an idea of implementing TDM for this 1 GHz signal. Is it possible, please explain from theoretical point of view and if possible, please help from MATLAB perspective. Thank you very much,

Homework Statement So we have just been learning limits which I understand, however there was one example which completely through me. It was regarding division by 0. We had just been learning the known limits such as lim x->infinity (1/x) = 0 which I understood, and how anything similar such...

Homework Statement I added an attachment... I am not understanding how they did this...

I have 2 matrices a=[1 2 3 4] and b=[1 4 9 16], i want to divide each term in matrix b by the same term in matrix a, in other words i want to end up with a matrix of [1 2 3 4]. Ive tried doing b/a, which clearly is wrong! Thanks for any help

Im given two polynomials: f(x) =(2x^6) + (x^5) - (3x^4) + (4x^3) + (x^2) -1 and g(x)=(x^3)-(x^2)+2x+3 find polynomials Q(x),R(x) in the set of R[x] s.t f(x) =g(x)Q(X) +R(X) and deg(R)<deg(g) Am i even in the right area? and something to do with manipulating numbers in C[x]...

Does it work ? Exp: (s power of 4) over (4 times s power of 4 plus 1) s^4 ---------- (4S^4)+1 LONG DIVISION : 1/4 _______ 4S^4+1√s^4...