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To divide the expression \( 4a^2 + 4ab - 2 \) by \( 2a \), we can do the division term by term:
1. Divide \( 4a^2 \) by \( 2a \):
\[
\frac{4a^2}{2a} = 2a
\]
2. Divide \( 4ab \) by \( 2a \):
\[
\frac{4ab}{2a} = 2b
\]
3. Divide \( -2 \) by \( 2a \):
\[
\frac{-2}{2a} = -\frac{1}{a}
\]
Now, combine the results from the three divisions:
\[
2a + 2b - \frac{1}{a}
\]
Thus, the quotient of \( \frac{4a^2 + 4ab - 2}{2a} \) is:
\[
\boxed{2a + 2b - \frac{1}{a}}
\]
So the correct response is:
**2a + 2b − 1/.