The remainder obtained when the polynomial x^ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to the Remainder Theorem,when a polynomial $P(x)$ is divided by $(x - a)$,the remainder is $P(a)$.Here,$P(x) = x^{64} + x^{27} + 1$ and

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) According to the Remainder Theorem,when a polynomial $P(x)$ is divided by $(x - a)$,the remainder is $P(a)$.Here,$P(x) = x^{64} + x^{27} + 1$ and the divisor is $(x + 1)$,which is $(x - (-1))$.Therefore,the remainder is $P(-1) = (-1)^{64} + (-1)^{27} + 1$.Since $64$ is an even number,$(-1)^{64} = 1$.Since $27$ is an odd number,$(-1)^{27} = -1$.Thus,the remainder is $1 + (-1) + 1 = 1 - 1 + 1 = 1$.

The remainder obtained when the polynomial $x^{64} + x^{27} + 1$ is divided by $(x + 1)$ is

Similar Questions

The remainder when $(11)^{1011} + (1011)^{11}$ is divided by $9$ is

The remainder when $7^{7^{7^{...7}}}$ ($22$ times $7$) is divided by $48$ is

The sum of the cubes of three consecutive natural numbers is divisible by

The remainder obtained when $5^{99}$ is divided by $13$ is

The expression $(1 + x)^n - nx - 1$ is divisible by (where $n \in N$ and $n > 1$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module