In particular: $x^3 - 4x^2 + 4x -2 $.
I would know what to do if it had one root which was an integer, however it does not.
any help is much appreciated, thank you.
2026-04-06 06:27:39.1775456859
How do I show a cubic polynomial does not factorise?
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All cubics with real coefficients factorize over the real polynomials. See the Fundamental Theorem of Algebra and its corollaries.
Not all cubics with integer coefficients factorize over the integer polynomials. However, if a cubic does factorize this way, one of the factors will be a linear polynomial. That means that there will be a rational root of the polynomial.
Therefore, for a cubic integer polynomial, use the Rational Root Theorem to find any rational roots. If there none, the cubic does not factor into polynomials with integer coefficients.