Question

5. Which polynomial is equal to (x^5+ 1) divided by (x + 1)?
AXA - X3 .x² - x + 1.
B X - X² + x² - x + 1
C x4 + x3 -- x2 + x + 1
D x + 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 = $(x+1)$

Now According to the rule of Division.

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

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

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

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

Step: 5 Now the remainder of step 4 will be new dividend which is $x+1$ and Divisor is $(x+1)$  when it is 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.