To analyze the expression \(3k + 2\), we can break down the options:
A. 3 times the sum of k and 2
This translates mathematically to \(3(k + 2)\) which simplifies to \(3k + 6\). This does not match \(3k + 2\).
B. 2 more than the quotient of 3 and k
This would be expressed as \(\frac{3}{k} + 2\) which does not match \(3k + 2\).
C. 2 more than 3 more than k
This translates to \(k + 3 + 2\) or \(k + 5\). This does not match \(3k + 2\).
D. 2 more than 3 times k
This is expressed as \(3k + 2\), which matches our original expression.
The correct answer is D: 2 more than 3 times k.