Question

if x²¹-20 is divided by x+1. find the remainder.​

Answer 1

Answer:

The remainder will be -21

Step-by-step explanation:

The given dividend is a polynomial of degree 21 and the divisor is a polynomial of degree 1 or simply a linear polynomial.

We know that, When a polynomial of higher degree is divided by another polynomial of a lower degree then the remainder will also be a polynomial whose degree is lesser than the degree of divisor.

Here the degree of the divisor is 1.

So, the degree of remainder must be less than 1 and also it must be a polynomial, so the only possible degree of the remainder is 0 i.e., the remainder is a constant.

Now,

Let Q(x) be the quotient and R be the remainder.

Then,

(x^21)-20=(x+1)Q(x)+R

Now, put x=-1

Then,

-1-20=(-1+1)(Q(-1))+R

-21=R

Therefore, the remainder is -21.

Hope this answer helps!