How to shorten an expression?

Question

Mathematics

How does x^3 + 3x^2 + 3x + 1 make (x+1)^3? That is, of course, you can come to such a reduction by sorting through various options, but is there any quick way to reduce such expressions? How is this done in complex equations?

Answer 1

There is no fast general way.
Any polynomial with real coefficients can be decomposed into a product of linear and quadratic factors with real coefficients ( wiki ). But the problem of finding this decomposition is equivalent to the problem of calculating all the roots of this polynomial, which (the problem) is unsolvable in radicals for polynomials of the fifth degree and higher.