Calculus/reminder

Advertisement

Expert: - 1/6/2010


Question
if f(x)/(x_1)=2 ; f(x)/(x-2)=3 find the reminder of
f(x)/((x-1)(x-2))

Answer
If the remainder when dividing by (x-1) is 2 and the remainder when dividing by (x-2) is 3,
it can be said that f(x) = I(x-1) + 2 and f(x) = J(x-2)+ 3 for integers I, J.

Looking at x=6, x-1=5 and x-2=4, so the number must be 7+20N for some integer N,
so the remainder when divided by (x-1)(x-2) would be 7.

If x=7, x-1=6 and x-2=5, so the number must be 8+40N for some integer N,
so the remainder when divided by (x-1)(x-2) would be 8.

f x=8, x-1=7 and x-2=6, so the number must be 9+56N for some integer N,
so the remainder when divided by (x-1)(x-2) would be 9.


From these, it can be shown that for any number x, the remainder is x+1

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.