What is the remainder when the polynomial P(x | vedclass

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

Question

(C) According to the Remainder Theorem,when a polynomial $P(x)$ is divided by $(x - a)$,the remainder is $P(a)$.Here,we are dividing by $(x - 1)$,so $

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(C) According to the Remainder Theorem,when a polynomial $P(x)$ is divided by $(x - a)$,the remainder is $P(a)$.Here,we are dividing by $(x - 1)$,so $a = 1$.We need to calculate $P(1)$:$P(1) = 1 + (1) + (1)^3 + (1)^9 + (1)^{27} + (1)^{81} + (1)^{243}$Since $1^n = 1$ for any positive integer $n$,we have:$P(1) = 1 + 1 + 1 + 1 + 1 + 1 + 1$$P(1) = 7$Therefore,the remainder is $7$.

What is the remainder when the polynomial $P(x) = 1 + x + x^3 + x^9 + x^{27} + x^{81} + x^{243}$ is divided by $x - 1$?

Similar Questions

Which of the following pairs of sets are equal? Justify your answer.
$X$,the set of letters in "$ALLOY$" and $B$,the set of letters in "$LOYAL$".

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${ x:x \text{ is a triangle in a plane} } \dots { x:x \text{ is a rectangle in the plane} }$

If $A = \{ 1, 2, 3, 4, 5 \}$,then what is the number of proper subsets of $A$?

Which of the following is a set? Justify your answer.
The collection of all boys in your class.

If $n(A) = 4$,$n(B) = 3$,and $n(A \times B \times C) = 24$,then find $n(C)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module