Question

Find the remainder when x^51 + 1 is divided by x+1.​

Answer 1

Concept Used :-

Remainder Theorem

Definition of remainder theorem

• Remainder theorem in algebra states that : If f(x) is a polynomial in x then the remainder on dividing f(x) by x − a is f(a).

$\large\underline{\bold{Solution :- }}$

$\rm :\longmapsto\:Let \: p(x) = {x}^{51} + 1$

Since,

• we have to find a remainder when p(x) is divided by x + 1.

Using remainder theorem,

• The remainder when p(x) is divided by x + 1 is

$\rm :\longmapsto\:remainder \: = \: p( - 1)$

$\rm :\longmapsto\:remainder \: = \: {( - 1)}^{51} + 1$

$\rm :\longmapsto\:remainder \: = - 1 + 1$

$\rm :\longmapsto\:remainder \: = \: 0$