remainder

1. Modulus Problem

Choose three integer numbers x, y, and z = c, respectively, where x>=1, y>=1, and z >=1 to get (a, b) pairs. The condition is (1<=a<=x, 1<=b<=y) where [ (a + b) % c = 0 ] , a and b are integer numbers. Note: % is modulus For example: x = 10, y = 5, z = 2 answer = 25 pairs I will show a few...
2. Confusion on Quotient and Remainder theroem

Find Remainder and Quotient a=39 b=-5 now solve like this a = b.q + r so 39 = -5 (q) + r 39 = -5 (-7) + (4) 39 = 35 + 4 39 = 39 but i am confuse please apology for if its my wrong understanding as per theorem "0" less than and equal to "r" less than "b" at above r is greater than b...

Hi; I'm factoring a polynomial using long division and end up with a quadratic x^2 - x - 6 + 18/x-3. When factoring this how do I handle the remainder? Thanks.
4. Casio fx-100AU PLUS - Remainder

Hi, Can anyone tell me if there is a way to find the remainder following division using this calculator. I am doing base conversions and need to show working by hand so if there is a quick way to find remainders that would be great. Kind regards Beetle
5. Finding the remainder

I am looking at an eay way to solve for the remainder of p(x) = x4 + 2x3 - x2 + x +2 is divided by (x+2) Any help on how to solve this would be great, I remember seeing a short cut on this skill but I can not remember where. Thanks,
6. Chinese theorem of remainder and flaws

Greetings,on my class i am given a system of congruence equations and my teacher told us that we can only solve this with chinese theorem if GCD = 1 now she showed us a way of solving it when GCD is not 1 without chinese theorem with extended euclid process but i can not find this online,can...
7. factor theorem and remainder theorem

Hi; Can someone tell me the difference between the factor theorem and the remainder theorem in polynomials? I know the remainder theorem but can't see a difference in the factor theorem. Thanks.
8. Remainder Theorem

The polynomial f(x) has a remainder of 2/1/2 when divided by (2x+1) and reminader of 13 when divided by (x-3) Find remainder when f(x) is divided by 2x^2 - 5x - 3 I know that f(-1/2) = 2/1/2 and f(3) = 13 and that 2x^2 - 5x - 3 is actually factorised to (2x+1)(x-3) How do I proceed...
9. Remainder Problem

What is the remainder when {32}^{32^{32} is divided by 7? The answer is 4. I wasn't able to get the remainder 4. I was getting a remainder 2 and we are not allowed to use modular arithmetic. How can we get the remainder 4 without using modular arithmetic. Please explain. Request advice on the...
10. factor and remainder theorem

if F(x)=x^4+2x^3+px^2-qx-12 can be expressed in the form of (x^2+x+2)^2-4(x+2)^2, find the values of p and q. therefore or else, find all the real roots and complex roots of equation f(x)=0. determine also set for real x such that f(x)>0
11. factor and remainder theorem

Find polynomial in x with degree 3, when x=-1, f(1)=0; when x=2,f(2)=0 when x =0, it is 8 and left remainder 16/3 when it is divided by 3x-2?
12. function-factor theorem and remainder theorem

Find polynomial in x with degree 3, when x=-1, f(1)=0; when x=2,f(2)=0 when x =0, it is 8 and left remainder 16/3 when it is divided by 3x-2?
13. Proving remainder of polynomial when divided by quadratic (remainder theorem)

Hello all I am having significant trouble with this question: If P(x) is divided by (x-a)(x-b), where a is not equal to b and a and b are elements of the real number set, prove that the remainder is [(P(b)-P(a))/(b-a)] x (x-a) + P(a) I was able to make some progress, but I am not able to...
14. remainder theorem help

The sum of the remainder when X^3 + (B+5)x + B is divided by x-1 and x+2 is 0. Find the value of B.... help needed. I dont even know how to start
15. Use Remainder Theorem for this problem?

Hi, I'm taking practice final exams for an online College Algebra course. One problem is stumping me. It says: The obvious (to me) approach is to use the Remainder Theorem and evaluate f(-3) to find the remainder. But there are two problems with that: 1. Every calculator I have is unable...
16. Find the remainder when 6341723110832864 is divided by 6 and 12?

I need to use the following rules to find the remainder but after solve it my answer is different from my books, so I need help and explanation in how to solve it. the rules I got is: r6 = 3r2 - 2r3 (mod 6) r12 = 4r3 - 3r4 (mod 12) xxx
17. Lagrange Remainder

My trouble is: How should I use it to prove/show what is requested to be so? With my kind regards, M.V.S/Kaemper
18. Chinese remainder theorem problem

\begin{cases} x \equiv 39 \pmod{189}\\ x \equiv 25 \pmod{539}\\ x \equiv 39 \pmod{1089}\end{cases} but two moduli are not pairwise prime (189, 1089)=3 What do we do to solve it then? Should we write prime decomposition for these moduli and calculate it separately? Thanks
19. P(x) leaves two remainder when divided by two polynomials , find r(x) when divided...

Let $p(x)$ be a polynomial. When $p(x)$ is divided by $x-1$, it leaves the remainder $4$. When it is divided by $x-2$ it leaves the remainder $5$. Then find the remainder when $p(x)$ is divided by $x^2-3x+2$. $p(1)=4$ $p(2)=5$ $\Rightarrow p(x)=x+3.$ [/TEX] I don't think I am right on...
20. remainder of p(x)/g(x) where g(x) is quadratic

The chapter is about Polynomials and the there are few questions on remainder theorem. If p(x) is divided by (ax-b) where a and b are constants, the remainder will be b/a. The teacher gave one extra out-of-portion question. Find the remainder when $x^{2014}+x^{2013}$ is divided by $x^2-1$...