<prompt> x3 - 3x2 4x - 1 ya aina nyingi ni x9 px6 qx3 r. Weka p,q,r p,q,r uliyoagiza mara tatu.  <response>: Acha alpha iwe mzizi wa x3 - 3x2 4x - 1 0, hivyo alpha3 3 alpha2 - 4 alpha 1. Kishaalpha4 3 alpha3 - 4 alpha2 alpha 3 3 alpha2 - 4 alfa 1 - 4 alpha2 alpha 5 alpha 2 - 11 alpha 3.Kwa hivyo,anzaalignalpha6 3 alpha2 - 4 alfa 12 9 alpha4 - 24 alpha3 22 alpha2 - 8 alpha 1 9 5 alpha2 - 11 alpha 3 - 24 3 alpha2 - 4 alpha 1 22 alpha2 - 8 alpha 1 -5 alpha2 - 11 alpha 4,mwishoalignnaanzaalignalpha9 alpha3 cdot alpha6 3 alpha2 - 4 alpha 1-5 alfa2 - 11 alpha 4 -15 alpha4 - 13 alpha3 51 alfa2 - 27 alpha 4 -15 5 alpha2 - 11 alpha 3 - 13 3 alpha2 - 4 alpha 1 51 alpha2 - 27 alpha 4 -63 alpha2 190 alpha - 54.mwishoalignKishaanzaalignalpha9 p alpha6 q alpha3 r -63 alpha2 190 alpha - 54 p -5 alpha2 - 11 alpha 4 q 3 alfa2 - 4 alfa 1 r -5p 3q - 63 alpha2 -11p - 4q 190 alpha 4p q r - 54.endalignTunataka hii ipungue hadi 0, kwa hivyo tunawekaanzaalign-5p 3q 63, 11p 4q 190, 4p q r 54.endalignKutatua, tunapata p,q,r 6,31,-1. Kwa thamani hizi, alpha9 p alpha6 q alpha3 r inapunguza hadi 0 kwa mzizi wowote wa alpha wa x3 - 3x2 4x - 1, hivyo x9 px6 qx3 r itagawanywa kwa x 3 - 3x2 4x - 1. 