Factoring Quadratic Polynomials

Can you tell a binomial from a trinomial?[br]And can you factor a quadratic binomial or trinomial?[br][br]Put yourself to the test and take the change to discover some "non-standard" factorizations!
Why can you factor [math]\left(25x^2+40x+16\right)[/math] both as [math]\left(5x+4\right)^2[/math] and [math]\left(-5x-4\right)^2[/math]?
Is it possible to factor the binomial [math]\left(x^2+16\right)[/math] over the set of real numbers?[br]If so, how would you factor it?
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Information: Factoring Quadratic Polynomials