Question

5. Which polynomial is equal to (x5 + 1) divided by (x + 1)?
A X – X3 -- x² - x + 1
B x4 – x3 + x2 -- x + 1
C x4 + x3 -- x2 + x + 1
D x4 + x3 + x2 + x + 1

Answer 1

Answer:

B  $x^4-x^3+x^2-x+1$

Step-by-step explanation:

Given,

Dividend = $(x^5+1)$

Divisor = $(x+1)$

Step 1: First The dividend is $(x^5+1)$ and Divisor is $(x+1)$ when divided first time the quotient will be $x^4$ and remainder will be $-x^4+1$

Step: 2 Now the new dividend is $-x^4+1$ and Divisor is $(x+1)$  when divided the quotient will be $x^4-x^3$ and remainder will be $x^3+1$

Step: 3 Now the new dividend is $x^3+1$ and Divisor is $(x+1)$  when divided the quotient will be $x^4-x^3+x^2$ and remainder will be $-x^2+1$

Step: 4 Now the new dividend is $-x^2+1$ and Divisor is $(x+1)$  when divided the quotient will be $x^4-x^3+x^2-x$ and remainder will be $x+1$

Step: 5 Now the new dividend is $x+1$ and Divisor is $(x+1)$  when divided the quotient will be $x^4-x^3+x^2-x+1$ and remainder will be 0.

Hence When the polynomial $(x^5+1)$ is divided by  $(x+1)$ the answer or quotient will be equal to  $x^4-x^3+x^2-x+1$ and remainder will be 0.