the remainder when x2014 + x2013 + x2012 + - Maths - Polynomials

Question

the remainder when x2014 + x2 013
+ x2012 + x + 1is divided by x + 1

Ashutosh Verma · Accepted Answer

Answer :

We have : x2014 + x2013 + x2012 + 
 + x +  1x +  1 , So we
write it , As :

⇒ x2014 + x2013 + x2012 +  x2011 + 
   + x2+ x +  1x +  1⇒ x2014  + x2012 + 
   + x2+ x2013+  x2011 + 
    + x +  1x +  1⇒ x  x2013+  x2011 + 
    + x + 1  x2013+  x2011 + 
    + x +  1x +  1⇒  x +  1   x2013+  x2011 + 
    + x +  1x +  1⇒   x2013+  x2011 + 
    + x  + 1x +  1

So,
Remainder will be = 1 ( Ans )

the remainder when x2014 + x2 013 + x2012 +...............x + 1is divided by x + 1

the remainder when x²⁰¹⁴ + x² ⁰¹³ + x²⁰¹² +...............x + 1is divided by x + 1