Answer:
Quotient = x^4 + x^3 + x^2 + x + 1
Remainder = 0
Step-by-step explanation:
(x^5 +1) is divided by (x - 1) as shown below:
(x^5 +1) / (x - 1)
where x^5 is divided by (x - 1) when multiplied by x^4 (quotient) to give x^4 - 1.
Now x^4 - 1 is divided by is divided by (x - 1) when multiplied by x^3 (quotient) to give x^3 - 1.
Then again x^3 - 1 is divided by (x - 1) when multiplied with x^2 (quotient) to give x^2 -1.
x^2 - 1 is divided by (x - 1) when multiplied by x to give (x - 1).
Lastly, (x - 1) is divided by (x - 1) when multiplied by 1 to cancel the terms with remainder 0.
