The time complexity described by the function \(4n^2 + 2n + 1\) can be expressed in Big O notation by focusing on the term with the highest degree, which governs the growth rate of the function as \(n\) becomes large.
The dominating term in this function is \(4n^2\). In Big O notation, we ignore constant factors and lower-order terms, so we can simplify \(4n^2\) to just \(n^2\).
Therefore, the Big O notation for the time complexity of the function \(4n^2 + 2n + 1\) is:
\[ \text{O}(n^2) \]
So the correct response is:
O(n^2)