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

B
`x^4-x^3+x^2-x+1`

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.