Factorisation of cyclotomic polynomials

[catcherintherye]

x^16 + 1 is irreducible over the rationals, correct?...


...also I am required to factorise the following polynomials

2) i) x^5 + 3x^4 + 2x^3 + x^2 -7

ii) x^5 + 10x^4 + 13x^3 -25x^2 -68x -60


now I would usually approach this using the factor theorem to find a factor and then divide by this factor and continue, however in the question I am told as a hint that I am to try substituting x-> x+h h=+-1, +-2, why all this is necessary i canot think?...

 

[Gib Z]

"x^16 + 1 is irreducible over the rationals, correct?..."

yup..

As for your hint, that is usually used to alter the roots of an equation. eg of the roots of a polynomial of degree 3 in x, is alpha, beta and gamma, subbing in x+1 will get you a polynomial that has roots alpha-1, beta -1 , gamma -1 etc etc.

Maybe that's a hint your ment to use creatively?