5x^3(3x + 2)
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(x2 - x + 1)(x2 + x + 1)
7/12
You can reduce the number by known factors to make it more manageable. Plus there are tricks for different numbers: If the number is even, then 2 is a factor. If the digits add up to a multiple of 3 then 3 is a factor. If the ones digit is a 5 or 0 (with a tens digit greater than or equal to 1), then 5 is a factor. If the ones digit is a 0 then 10 is a factor. If the digits have the property that the first minus the second, plus the third, minus the fourth, (alternating signs) equals 0, then 11 is a factor. There are other tricks but these factors would be the most common.
(x^2 - 2x + 2)(x^2 + 2x + 2)
(x2 + 3x + 5)(x2 - 3x + 4)