factoring quadratic with leading coefficient of -1 and both values are the same

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So I have to factor this quadratic:

$-x^2 + 4$

I've rewritten it as:

$-x^2 + 0x + 4$

Then the factors that add to 0 and multiply to 4 are 2 and -2, so is the answer $-(x + 2)(x - 2)$ or $-(x - 2)(x + 2)$

Also, another question I have is the answer was written by the professor as:

$(2 - x)(2 + x)$

Which I just don't understand. Is that just another way of writing one of the above factorizations?