SOLUTION: Find the remainder when p(x) is divided by q(x), where p(x) = x^5 + 1 and q(x) = x^2 + x + 2.

Question 1209680: Find the remainder when p(x) is divided by q(x), where p(x) = x^5 + 1 and q(x) = x^2 + x + 2.

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to find the remainder using polynomial long division:
```
x^3 - x^2 - x + 1
----------------------------------
x^2 + x + 2 | x^5 + 0x^4 + 0x^3 + 0x^2 + 0x + 1
x^5 + x^4 + 2x^3
------------------
-x^4 - 2x^3 + 0x^2
-x^4 - x^3 - 2x^2
------------------
-x^3 + 2x^2 + 0x
-x^3 - x^2 - 2x
------------------
3x^2 + 2x + 1
3x^2 + 3x + 6
------------------
-x - 5
```
Therefore, the remainder when p(x) is divided by q(x) is -x - 5.

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