Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
What is the remainder when x^23 is divided by x^2-3x+2 ?
Dear Vignesh,Solution:- x^2 - 3x + 2 can be written as (x-1)(x-2)
Also, x^23 can be written as [2(x-1) - (x-2)]23, which on Binomial expansion will give-
[2(x-1) - (x-2)]23 = [2(x-1)]23 + (-1) 23C1[2(x-1)]22 [(x-2)] + (-1)2 23C2[2(x-1)]21 [(x-2)]2 +.....(-1)22 23C22[2(x-1)] [(x-2)]22 + (-1)23 23C23 [(x-2)]23
As we can see, all the terms except first and last contains atleast one (x-1) and (x-2).
So, the terms that are not divisible by (x-1)(x-2) are [2(x-1)]23 and (-1)23 23C23 [(x-2)]23
Remainder = { [2(x-1)]23 + (-1)23 23C23 [(x-2)]23 } /(x-1)(x-2)
= { [2(x-1)]22 /(x-2)} - {[(x-2)]22 /(x-1)}Please feel free to post as many doubts on our discussion forum as you can. If you find any questionDifficult to understand - post it here and we will get you the answer and detailed solution very quickly. Weare all IITians and here to help you in your IIT JEE preparation.All the best Vignesh!!!Regards,Askiitians ExpertsPriyansh Bajaj
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !