<prompt> Acha px iwe polynomial ya shahada ya 6 hivyop2n frac12nkwa n 0, 1, 2, dots, 6. Tafuta p0.  <response>: Acha qx xpx - 1. Kisha qx ina digrii 7, na q2n 0 kwa n 0, 1, 2, dots, 6, hivyoqx cx - 1x - 2x - 22 dotsm x - 26kwa c.Tunajua kwamba q0 0 cdot p0 - 1. Kuweka x 0 katika equation hapo juu, tunapataq0 c-1-2-22 dotsm -26 -221 c,hivyo c frac1 221. Kwa hiyo,anzaalignqx fracx - 1x - 2x - 22 dotsm x - 26221 x - 1 kushoto fracx2 - 1 kulia kushoto fracx22 - 1 kulia dotsm left fracx 26 - 1 kulia.endalignKibali cha x katika qx ni basianzaalign1-1-1 dotsm -1 kushoto -1 kushoto frac12 kulia -1 dotsm - 1 kulia kushoto -1-1 kushoto frac122 kulia dotsm -1 kulia kushoto -1 dotsm -1 kushoto -frac126 kulia kulia 1 frac12 frac122 dots frac126 frac1 - frac12 71 - frac12 2 - frac164 frac12764.endalignPia, mgawo thabiti katika qx ni -1, kwa hivyo qx ni wa fomuqx frac1221 x7 vitone frac12764 x - 1.Kishapx fracqx 1x frac1221 x6 vitone frac12764. Kwa hivyo, p0 frac12764. 