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.