Thursday, 28 September 2017

abstract algebra - Trick for reducing a specific polynomial.



Let f(x)=x4x3+2x23x3



Show that f(x) is reducible over Q



Rational zeros shows there is no roots i tried writing (x2+bx+c)(x2+dx+e) and then tried to solve the equations for each of letters but it got crazy ugly which lead me to the conclusion there must be a better way...


Answer




i think that is a good idea, it is (x2+3)(x2x1)=f(x)


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