Explanation

To factorize 4x² + 7x + 3:

Let's find two numbers that multiply to 4*3 = 12 and add to 7:

The numbers are 4 and 3 (since 4 + 3 = 7 and 4 * 3 = 12).

Now, rewrite the middle term:

4x² + 4x + 3x + 3

Factor by grouping:

4x(x + 1) + 3(x + 1)

(4x + 3)(x + 1)

The correct answer is (x + 1)(4x + 3).