# 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 $x^2-1$...