<prompt> Pata nonzero monic polynomial Px yenye coefficients kamili na digrii ndogo kama P1-sqrt32sqrt340. Polynomia inaitwa textitmonic ikiwa mgawo wake mkuu ni 1.  <response>: Acha x 1 - sqrt32 sqrt34. Kumbuka kwamba 1 - sqrt32 sqrt34 1 sqrt32 3, hivyox frac31 sqrt32.Kishafrac3x 1 sqrt32,hivyofrac3x - 1 frac3 - xx sqrt32.Tunapata mraba wa pande zote mbili.frac-x3 9x2 - 27x 27x3 2,hivyo -x3 9x2 - 27x 27 2x3. Hii hurahisisha hadi 3x3 - 9x2 27x - 27 3x3 - 3x2 9x - 9 0, ili tuweze kuchukuafx x3 - 3x2 9x - 9. 