<prompt> Kuna polynomial P kama kwamba kwa kila nambari halisi x, x512 x256 1 x2 x 1 Px. Wakati P inaandikwa katika umbo la kawaida la polinomia, ni viambajengo vyake vingapi ambavyo ni nonzero?  <response>: Tunaweza kuandikaanzaalignx512 x256 1 x512 - x2 x256 - x x2 x 1 x2 x510 - 1 x x255 - 1 x2 x 1 x2 x3 - 1x507 x504 x501 dots x3 1 quad x x3 - 1x252 x249 x246 vitone x3 1 quad x2 x 1 x - 1x2 x 1x509 x506 x503 vitone x5 x2 quad x - 1x2 x 1x253 x250 x247 vitone x4 x quad x2 x 1 x2 x 1x510 - x509 x507 - x506 x504 - x503 dots x6 - x5 x3 - x2 quad x2 x 1x254 - x253 x251 - x250 x248 - x247 vidoti x5 - x4 x2 - x quad x2 x 1.mwishoalignHivyo,anzaalignPx x510 - x509 x507 - x506 x504 - x503 dots x6 - x5 x3 - x2 quad x254 - x253 x251 - x250 x248 - x247 vitone x5 - x 4 x2 - x 1 x510 - x509 x507 - x506 vitone x258 - x257 quad x255 - x254 x252 - x251 vitone x3 - x2 quad x254 - x253 x251 - x250 vitone x2 - x 1 x510 - x509 x507 - x506 vitone x258 - x257 quad x255 - x253 x252 - x250 vitone x3 - x 1.endalignKati ya x510, -x509, x507, -x506, dots, x 258, -x257, kuna vigawo 170 vya nonzero.Miongoni mwa x255, -x253, x252, -x250, dots, x3, -x, kuna mgawo mwingine 170 wa nonzero.Muhula wa mwisho wa 1 unatupa jumla ya 341 nonzero coefficients. 