In order to find the quotient and remainder of the division, let's divide the polynomials doing the following steps:
x³ divided by x: x².
x² times (x + 2): x³ + 2x²
x³ + 6x² + 17x + 11 minus (x³ + 2x²): 4x² + 17x + 11
4x² divided by x: 4x
4x times (x + 2): 4x² + 8x
4x² + 17x + 11 minus (4x² + 8x): 9x + 11
9x divided by x: 9
9 times (x + 2): 9x + 18
9x + 11 minus (9x + 18): -7
Therefore the quotient is x² + 4x + 9 and the remainder is -7
Correct option: first one.