To factor the quadratic expression \(2x^2 + 7x + 3\), we can use the method of factoring by grouping or finding two numbers that multiply to \(2 \times 3 = 6\) and add up to \(7\).
The factors of \(6\) that add up to \(7\) are \(6\) and \(1\).
So, we can rewrite the quadratic as follows:
\[ 2x^2 + 6x + x + 3 \]
Next, we can group the terms:
\[ (2x^2 + 6x) + (x + 3) \]
Now, factor out the common terms from each group:
\[ 2x(x + 3) + 1(x + 3) \]
Now we can factor out the common binomial factor:
\[ (2x + 1)(x + 3) \]
Thus, the factored form of the quadratic expression \(2x^2 + 7x + 3\) is:
\[ (2x + 1)(x + 3) \]
Therefore, the correct response is:
(2x+1)(x+3)