Which is the completely factored form of 4x² + 28x + 49?

To find the completely factored form of the quadratic expression 4x² + 28x + 49, we can follow these steps:

1. First, we look for common factors in the coefficients. Here, the leading coefficient is 4, which can be factored out.
2. Rearranging, we get:

4(x² + 7x + 12)

3. Next, we need to factor the quadratic expression inside the parentheses, x² + 7x + 12. We want to find two numbers that multiply to 12 and add to 7.
4. Those two numbers are 3 and 4. Therefore, we can rewrite the quadratic as:

(x + 3)(x + 4)

5. Now, substituting this back into our expression gives us:

4(x + 3)(x + 4)

6. Thus, the completely factored form of the original expression is:

4(x + 3)(x + 4)

This means that when you multiply out 4(x + 3)(x + 4), you’ll arrive back at the original expression 4x² + 28x + 49.