Question

if x^21 - 20 is divided by x+1, find the remainder

Answer 1

x^21-20
put x=-1
-1^21-20
=-1-20
=-21

Answer 2

Given:

if x^21 - 20 is divided by x+1

To Find:

find the remainder

Solution:

The following question can be solved using the Remainder theorem.

A remainder theorem is a theorem that states that if a polynomial P(x) is divided by a linear equation of the form (x-a) then the value P(a) will give the remainder.

So in the given question, the polynomial is

$P(x)=x^{21}-20$

is divided by x+1, so the value of P(-1) will give the remainder when x^21-20 is divided by x+1,

[tex]P(-1)=(-1)^{21}-20\\ =-1-20\\ =-21[/tex]

Hence, the remainder will be -21.