Remainder Definition and 171 Threads

Find a polynomial of degree three that when divided by x - 2 has a remainder of 3. You will really have to think on this one. Hint: Work backwards! ok here's the thing I've tried I've looked at other problems but I can barely work problems forward, backwards...well your talking to me here my...

The task is to find the remainder of the equation: \frac{18^2+2^{100}}{11} Now I know that if a \equiv b\ (mod\ m),\ c \equiv d\ (mod\ m) \Rightarrow a + c \equiv b +d\ (mod\ m) and ac \equiv bd\ (mod\ m) so 18^2 \equiv b\ (mod\ 11) \Rightarrow \frac{18^2}{11}=29.454545... \Rightarrow...

What is the remainder?? Homework Statement What is the remainder when (a+b+c)^333-a^333-b^333-c^333 is divided by (a+b+c)^3-a^3-b^3-c^3? Homework Equations None The Attempt at a Solution I tried this (a+b+c)^333-a^333-b^333-c^333 = Q{(a+b+c)^3-a^3-b^3-c^3}+h where h is the...

Homework Statement Use the Remainder Estimation Theorem to find an interval containing x=0 over which f(x) can be approximated by p(x) to three decimal-place accuracy throughout the interval. Check your answer by graphing |f(x) - p(x)| over the interval you obtained. f(x)= sinx p(x)=...

Okay, I made this program in order to solve this question What is the smallest positive integer x such that x^2 + 3x + 5 is divisible by 121? The program complies perfectly. But when I execute it, it don't print out any answer. import java.math.BigInteger; public class Number37 { public...

remainder theorem...? Find the value of 'a' and 'b' and the remaining factor if the expression ax^3-11x^2+bx+3 is divisible by x^2-4x^2+3 do i simplify x^2-4x^2+3 and then substitute for x? im so lostt!

How many terms of the series do we need to add in order to find the sum to the indicated accuracy? \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^{2}} , | error | < 0.01 . So, b_{n} = \frac{1}{n^{2}} . b_{n} < b_{n+1} , and \lim_{n\rightarrow \infty} b_{n} = 0 . Therefore, the series is...

Two questions, first, I solved something, but I was just playing around with the numbers, and I didn't really know what I was doing, nor did I really understand it after I was done. The question is as follows: When x + 2 is divided into f(x), the remainder is 3. Determine the remainder when x...

Chinese Remainder Theorem! I'm pretty sure that the following is in fact the Chinese remainder Theorem: If n= (m1)(m2)...(mk) [basically, product of m's (k of them)] where each m is relatively prime in pairs, then there is an isomorphism from Zn to ( Zm1 X Zm2 X ... X Zmk). Zn...

Can anyone help me? I'm trying to find the remainder when 111111222222 is divided by 7 without using any long division. I thinking that i can take the alternating sums of the 3 digits blocks and set that mod7. I'm not sure if I'm on the right track or not. thanks

7a) f(x0 = 2x3+32-6x+1 Find the remainder when F(x) is divided by (2x-1) b) (i) Find the remainder when f(x) is divided by (x+2) (ii) Hence, or otherwise solve the equation: 2x3+32-6x-8=0 giving your answer to two decimal places. This is what I've done: a) r= -1 (i did f(1/2) to get...

Q. What is the remainder when 23 raised to 98 is divided by 98?Why?

I'm having a lot of trouble setting up the equations for the following question where I need to use the chinese remainder theorem. Q. Fifteen pirates steal a stack of identical gold coins. When they try to divide them evenly, two coins are left over. A fight erupts and one of the pirates is...

It is given that f(x)=8x^3+4x-3. The question is: Find the remainder when 1/f(x) is divided by x+1. My textbook says the remainder does not exist? I just can't solve it. Thanks in advance for any help. Abdullah

whats the remainder when x^X^x^x... is divided by x-700^(1/700) leaving answer in whole number

I have 2 questions. 1)what is the remainder with 100! is divided by 103? explain your answer 2)a = 238000 = 2^4 x 5^3 x 7 x 17 and b=299880 = 2^3 x 3^2 x 5 7^2 17. Is there an integer so that a divides b^n? if so what is the smallest possibility for n? the first one i have no...

I'm not really sure about such things, but this is my question. :smile: Say a photon of white light in incident on an object which is instrinically a blue object, just any regular blue object. Now (naturally) you see light (a photon corresponding with a wavelength that matches the blue...

Given that a polymial p(x) is p(x)= (x-1)(x-2) q(x) + 2x+3 where q(x) is also a polynomial Find the remainder when p(x) is divided by (x-1)(x+2) where the remainder divided by (x-1) and (x+2) is both 5 and 7 respectively. I don't know even where to start ! so please help, thanks alot.

hi all I am new on the forum I wonder if is possible to find a method that proofs that a number IS NOT a solution of a set of congruences Maybe using the chinese remainder theorem?? best regards japam

If p(x) = (x+2)(x+k) and if the remainder is 12 when p(x) is divided by x-1, then what is the value of k?

If p^2 is exactly divisible by p+q, then proof q^2 is exactly divisible by p+q. How do I proof this, and how do I apply the remainder theorem? I know if f(x) = x^2 + 2x + 1, since f(-1) = 0 there fore (x + 1) is a factor of f(x). So in this case p^2 = p x p or p^2 x 1...