From the provided image, we are working with the function $f(x) = x^2 + 6x + 4$. The question asks us to find the zeros of this function and identify its factorization.

Solution:

To factorize $f(x) = x^2 + 6x + 4$, let's proceed as follows:

1. Use the quadratic formula to find the roots: The quadratic formula is: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ Here, $a = 1$, $b = 6$, $c = 4$.

   Substituting: $x = \frac{-6 \pm \sqrt{6^2 - 4(1)(4)}}{2(1)}$ $x = \frac{-6 \pm \sqrt{36 - 16}}{2}$ $x = \frac{-6 \pm \sqrt{20}}{2}$ $x = \frac{-6 \pm 2\sqrt{5}}{2}$ $x = -3 \pm \sqrt{5}$

   The roots are $x = -3 + \sqrt{5}$ and $x = -3 - \sqrt{5}$.

2. Factorize the quadratic: The factorization of $f(x)$ can be written using the roots: $f(x) = (x - (-3 + \sqrt{5}))(x - (-3 - \sqrt{5}))$ $f(x) = (x + 3 - \sqrt{5})(x + 3 + \sqrt{5})$

   This matches with none of the multiple-choice options in the image.

3. Check provided factorizations: By expanding each of the options, none result in $x^2 + 6x + 4$. Therefore, the correct choice is "None of these."

Let me know if you want further clarification or detailed steps!

Here are 5 related questions for practice:

1. How can you complete the square to rewrite $x^2 + 6x + 4$?
2. How do you derive the quadratic formula?
3. What are the key steps to graph $x^2 + 6x + 4$?
4. How do the zeros of a function relate to its graph?
5. How can you verify a factorization is correct?

Tip: When factorizing, always verify by expanding the factors to ensure they produce the original polynomial!