<prompt> Acha Px iwe nonzero polynomial kiasi kwamba x-1Px1x2Px kwa kila x halisi, na leftP 2kulia2 P3. Tafuta Ptfrac72.  <response>: Kuweka x 1, tunapata0 3P1,kwa hivyo Px ina kipengele cha x - 1.Kuweka x -2, tunapata-3 P-1 0,kwa hivyo Px ina kipengele cha x 1.Kuweka x 0, tunapata-1 P1 2P0.Kwa kuwa P1 0, P0 0, ina maana P0 ina kipengele cha x.HebuPx x - 1x 1x Qx.Kishax - 1xx 2x 1 Qx 1 x 2x - 1x 1x Qx.Hii hurahisisha hadi Qx 1 Qx.KishaQ1 Q2 Q3 Q4 dotsb.Kwa kuwa Qx Q1 kwa thamani nyingi sana za x, Q x ni lazima liwe polima isiyobadilika. Acha Qx c, hivyoPx cx - 1x 1x.Kisha P2 6c na P3 24c, hivyo6c2 24c.Kutatua, tukikumbuka kwamba c neq 0, tunapata c frac23. Kisha Px frac 23 x - 1x 1x, naP kushoto frac72 kulia frac23 cdot frac52 cdot frac92 cdot frac 72 frac1054. 