How do you solve (x3 + 6x2 + 3x + 1) : (x - 2)

We conduct long division, cancelling each term in x³ + 6x² + 3x + 1. As so:

x² (x - 2) = x³ - 2x²

Subtracting from the original equation, we get:

8x² + 3x + 1

8x (x - 2) = 8x² - 16x

Subtracting from the new equation, we get:

21x + 1

21 (x - 2) = 21x - 42

Subtracting from the new equation, we get:

43

The answer is x² + 8x + 21 with a remainder of 43.