KVPY SA Exam 05-Nov-2017 Question Paper

Question : 10 of 80

Marks: +1, -0

Let r(x) be the remainder when the polynomial

x^135 + x^125 -x^115 + x^5 + 1

is divided by

x^3 -x.

Then

Solution:

x^135 + x^125 -x^115 + x^5 + 1

=k(x^3 -x) + Ax^2 + Bx + C

put x = 0 [C = 1]
Put x = 1
3 = A + B + 1
A + B = 2 .....(i)
put x = –1
–1 = A – B + 1
A – B = –2 .....(ii)
(i) + (ii)
A = 0
B = 2

Go to Question:

Prev Question

Next Question