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CAPITULO VII

Teorema del Residuo
Ejercicio 74
Hallar sin efectuar la división, el residuo de dividir:
  1. x 2 2x+3 entre x1
    x1 =0 x =1 x 2 2x+3 = ( 1 ) 2 2( 1 ) +3 =12+3 =2
  2. x 3 3 x 2 +2x2 entre x+1
    x+1 =0 x =1 x 3 3 x 2 +2x2 = (1 ) 3 3 (1 ) 2 +2(1 ) 2 =1322 =8
  3. x 4 x 3 +5 entre x2
    x2 =0 x =2 x 4 x 3 +5 = ( 2 ) 4 ( 2 ) 3 +5 =168+5 =13
  4. a 4 5 a 3 +2 a 2 6 entre a+3
    a+3 =0 a =3 a 4 5 a 3 +2 a 2 6 = (3 ) 4 5 (3 ) 3 +2 (3 ) 2 6 =815(27 ) +2( 9 ) 6 =81+135+186 =228
  5. m 4 + m 3 m 2 +5 entre m4
    m4 =0 m =4 m 4 + m 3 m 2 +5 = ( 4 ) 4 + ( 4 ) 3 ( 4 ) 2 +5 =256+6416+5 =309
  6. x 5 +3 x 4 2 x 3 +4 x 2 2x+2 entre x+3
    x+3 =0 x =3 x 5 +3 x 4 2 x 3 +4 x 2 2x+2 = (3 ) 5 +3 (3 ) 4 2 (3 ) 3 +4 (3 ) 2 2(3 ) +2 = 243 + 243 2(27 ) +4( 9 ) +6+2 =54+36+8 =98
  7. a 5 2 a 3 +2a4 entre a5
    a5 =0 a =5 a 5 2 a 3 +2a4 = ( 5 ) 5 2 ( 5 ) 3 +2( 5 ) 4 =31252( 125 ) +104 =3131250 =2881
  8. 6 x 3 + x 2 +3x+5 entre 2x+1
    2x+1 =0 2x =1 x = 1 2 6 x 3 + x 2 +3x+5 =6 ( 1 2 ) 3 + ( 1 2 ) 2 +3( 1 2 ) +5 =( 1 ) + 1 4 3 2 +5 = 3 4 + 1 4 3 2 +5 = 3+16+20 4 = 4 =3
  9. 12 x 3 21x+90 entre 3x3
    3x3 =0 3x =3 x = 3 3 x =1 12 x 3 21x+90 =12 ( 1 ) 3 21( 1 ) +90 =1221+90 =81
  10. 15 x 3 11 x 2 +10x+18 entre 3x+2
    3x+2 =0 3x =2 x = 2 3 15 x 3 11 x 2 +10x+18 =15 ( 2 3 ) 3 11 ( 2 3 ) 2 +10( 2 3 ) +18 =( 8 ) 11( 4 9 ) 20 3 +18 = 40 9 44 9 20 3 +18 = 404460+162 9 = 9 =2
  11. 5 x 4 12 x 3 +9 x 2 22x+21 entre 5x2
    5x2 =0 5x =2 x = 2 5 5 x 4 12 x 3 +9 x 2 22x+21 =5 ( 2 5 ) 4 12 ( 2 5 ) 3 +9 ( 2 5 ) 2 22( 2 5 ) +21 = 5 ( 16 5 ) 12( 8 125 ) +9( 4 25 ) 44 5 +21 = 16 125 96 125 + 36 25 44 5 +21 = 1696+1801100+2625 125 = 125 =13
  12. a 6 + a 4 8 a 2 +4a+1 entre 2a+3
    2a+3 =0 2a =3 a = 3 2 a 6 + a 4 8 a 2 +4a+1 = ( 3 2 ) 6 + ( 3 2 ) 4 8 ( 3 2 ) 2 +( 3 2 ) +1 = 729 64 + 81 16 ( 9 4 ) 6+1 = 729 64 + 81 16 185 = 729 64 + 81 16 23 = 729+3241472 64 = 419 64