1 ESERCIZI Operare con numeri e lettere 212 (8x3 4x2 + 16x 2) : (2x + 3) [q(x) = 4x2 8x + 20; r = 62] 213 ( 2x3 3x + x4 + x2 + 3) : (x3 x2 3) [q(x) = x 1; r = 0] 214 (2x4 1 3x3) : ( 1 x x2) [q(x) = 2x2 + 5x 3; r(x) = 2x 4] 215 (x6 6x + 5) : (x2 2x + 1) [q(x) = x4 + 2x3 + 3x2 + 4x + 5; r = 0] 216 (2x5 x4 3x3 x 1) : (x3 2x 1) [q(x) = 2x2 x + 1; r = 0] 217 (6x4 11x3 + 25x2 17x + 19) : (2x2 3x + 4) [q(x) = 3x2 x + 5; r(x) = 2x 1] 218 (4x4 + 2x3 2x2 + 9x + 5) : ( 2x3 + x 5) [q(x) = 2x 1; r = 0] 219 (1 + 2x 2x2 5x3 2x4) : (x3 + 2x2 1) [q(x) = 2x 1; r = 0] 220 (2x4 + 4x2 8x + 16) : (2x2 4x + 4) [q(x) = x2 + 2x + 4; r = 0] 221 (x5 7x4 + 12x3 x2 + 7x 12) : (x2 + x + 1) [q(x) = x3 8x2 + 19x 12; r = 0] 222 (t4 3t3 + t2 + 3t 2) : (t + 2 t2) [q(t) = t2 + 2t 1; r = 0] 223 x4 : (x2 + x + 1) 224 [q(x) = x2 x; r(x) = x] 2 2 _1_ 3 ( 5 x + 5x + 1) : (x 1) _1_ _1_ [q(x) = 5 x + 5; r(x) = 5 x + 6] Regola di Ruffini Effettua le seguenti divisioni utilizzando la regola di Ruffini. esercizio svolto 4 3 2 (2x 4x + x 4x + 3) : (x 2) 2 4 +1 4 +3 4 +2 2 0 +2 4 0 +1 2 1 Il quoziente e il resto sono, dunque, rispettivamente: q(x) = 2 x3 + 1x 2 = 2 x3 + x 2 r = 1 225 (x2 2x + 1) : (x 1) [q(x) = x 1; r = 0] 227 (3x2 + 5x + 2) : (x 1) [q(x) = 3x + 8; r = 10] 226 (x2 3x + 2) : (x 1) [q(x) = x 2; r = 0] 228 (2x2 5x + 1) : (x 2) [q(x) = 2x 1; r = 1] 229 (x3 5x2 + x + 1) : (x + 1) 230 (x3 2x2 + 4) : (x 2) 231 (x4 x3 + x2 x + 1) : (x 1) 232 (2x5 2x4 3x3 4x2 + 2x 1) : (x 1) 233 (x5 + x4 + x3 + x2 + x + 1) : (x + 1) [q(x) = x2 6x + 7; r = 6] [q(x) = x2; r = 4] [q(x) = x3 + x; r = 1] [q(x) = 2x4 3x2 7x 5; r = 6] [q(x) = x4 + x2 + 1; r = 0] 59