<prompt> Acha a 0, na Px iwe polinomia yenye viambajengo kamili kama vileP1 P3 P5 P7 anaP2 P4 P6 P8 -a.Je, thamani ndogo zaidi ya a ni ipi?  <response>: Lazima kuwe na aina fulani ya Qx kiasi kwamba Px-ax-1x-3x-5x-7Qx.Kisha , ikichomeka thamani za 2,4,6,8, tunazopataP2-a2-12-32-52-7Q2 -15Q2 -2a,P4 -a4-14-34-54-7Q4 9Q4 -2a,P6-a6 -16-36-56-7Q6 -15Q6 -2a,P8-a8-18 -38-58-7Q8 105Q8 -2a.Yaani,-2a-15Q29Q4-15Q6105Q8.Hivyo, a lazima iwe kizidishio cha textlcm15,9, 15,105315.Sasa tunaonyesha kuwa kuna Qx kiasi kwamba a315. Kuweka thamani hii kwenye mlinganyo ulio hapo juu kunatupaQ242, quad Q4-70, quad Q642, quad Q8-6.From Q2 Q6 42, QxRxx-2x-642 kwa baadhi ya Rx. Tunaweza kuchukua Rx -8x 60 , ili Qx itoshe Q4 -70 na Q8 -6.Kwa hiyo, jibu letu ni 315. 