Factoring quadratic equations relies on the distributive property. In particular, note that for any quadratic, we can find factors such that:

\[ ax^2 + bx +c = Q(x+R)(x+S). \]

For example: \( 2x^2 + 10x + 12 = 2\left[(x+2)(x+3) \right] \).

It is worth noting that some polynomials cannot be factored using only real numbers. For example, \( x^2 + 1 =0 \) does not have any real-numbered factors.

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