Fastest way to factor binomials and trinomials?

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Synthetic division and recognition.

Synthetic division for higher degree polynomials which may/may not be factored into binomials.

Recognition for difference of two squares, perfect squares, difference of cubes, sums of cubes, etc. Also any polynomials which can blatantly be factored.

Oh and also keep in your head coefficients. Binomial expansion follows Pascal's triangle for perfect powers.
 
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