Question

The remainder when x^2001 + 2 is divided by x² - 4 is

Answer 1

ANSWER: 4x+2^2001+2

Step-by-step explanation:

x^2001+2=ax+b  (dividend = divisor*qu. + re.)

factorising x^2-4 we get (x-2)(x+2)

for x=2

2^2001+2=2a+b       equation 1

for x=-2

-2^2001+2=-2a+b    equation 2

solving equation 1 and equation 2

2^2001+2=2a+b

-2^2001+2=-2a+b

a=4

b=2^2001-4

so the remainder is ax+b=4x+2^2001-4