What method would you use to factor the following polynomial?4 + 8x2

To factor the polynomial 4 + 8x^2, you can use the method of factoring by grouping. However, in this case, the polynomial is already in its simplest form and cannot be factored further using real numbers.

If you want to factor it over the complex numbers, you can use the difference of squares method. Here's how:

1. Rewrite the polynomial in the form of a^2 - b^2, which is a difference of squares. In this case, you can rewrite 4 + 8x^2 as (2i)^2 - (sqrt(8)x)^2.

2. Apply the difference of squares formula, which states that a^2 - b^2 = (a - b)(a + b). In this case, you get (2i - sqrt(8)x)(2i + sqrt(8)x).

So, the polynomial 4 + 8x^2 factored over the complex numbers is (2i - sqrt(8)x)(2i + sqrt(8)x).