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Ejercicio 99

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CAPITULO X

Descomposición Factorial
Ejercicio 99
Factorar:
  1. x 4 +5 x 2 +4 =( x 2 + ) ( x 2 + ) . 4 1 | 4 =( x 2 +4 ) ( x 2 +1 )
  2. x 6 –6 x 3 –7 =( x 3 – ) ( x 3 + ) . 7 1 | 7 =( x 3 –7 ) ( x 3 +1 )
  3. x 8 –2 x 4 –80 =( x 4 – ) ( x 4 + ) . 80 40 20 10 1 | 2 2 2 10 =( x 4 –10 ) ( x 4 +8 )
  4. x 2 y 2 +xy–12 =( xy+ ) ( xy– ) . 12 6 3 1 | 2 2 3 =( xy+4 ) ( xy–3 )
  5. ( 4x ) 2 –2( 4x ) –15 =( 4x– ) ( 4x+ ) . 15 5 1 | 3 5 =( 4x–5 ) ( 4x+3 )
  6. ( 5x ) 2 +13( 5x ) +42 =( 5x+ ) ( 5x+ ) . 42 21 7 1 | 2 3 7 =( 5x+6 ) ( 5x+7 )
  7. x 2 +2ax–15 a 2 =( x+ ) ( x– ) . 15 5 1 | 3 5 =( x+5a ) ( x–3a )
  8. a 2 –4ab–21 b 2 =( a– ) ( a+ ) . 21 7 1 | 3 7 =( 7a–7b ) ( 7a+3b )
  9. ( x–y ) 2 +2( x–y ) –24 =[ ( x–y ) + ] [ ( x–y ) – ] . 24 12 6 1 | 2 2 6 =[ ( x–y ) +6 ] [ ( x–y ) –4 ] =( x–y+6 ) ( x–y–4 )
  10. 5+4x– x 2 =–( x 2 –4x–5 ) =–( x– ) ( x+ ) . 5 1 | 5 =–( x–5 ) ( x+1 ) =( 5–x ) ( x+1 )
  11. x 10 + x 5 –20 =( x 5 + ) ( x 5 – ) . 20 10 5 1 | 2 2 5 =( x 5 +5 ) ( x 5 –4 )
  12. m 2 +mn–56 n 2 =( m+ ) ( m– ) . 56 28 14 7 1 | 2 2 2 7 =( m+8n ) ( m–7n )
  13. x 4 +7a x 2 –60 a 2 =( x 2 + ) ( x 2 – ) . 60 30 15 5 1 | 2 2 3 5 =( x 2 +12a ) ( x 2 –5a )
  14. ( 2x ) 2 –4( 2x ) +3 =( 2x– ) ( 2x– ) . 3 1 | 3 =( 2x–3 ) ( 2x–1 )
  15. ( m–n ) 2 +5( m–n ) –24 =[ ( m–n ) + ] [ ( m–n ) – ] . 24 12 6 3 1 | 2 2 2 3 =[ ( m–n ) +8 ] [ ( m–n ) –3 ] =( m–n+8 ) ( m–n–3 )
  16. x 8 + x 4 –240 =( x 4 + ) ( x 4 – ) . 240 120 60 30 15 1 | 2 2 2 2 15 =( x 4 +16 ) ( x 4 –15 )
  17. 15+2y– y 2 =–( y 2 –2y–15 ) =–( y– ) ( y+ ) . 15 5 1 | 3 5 =–( y–5 ) ( y+3 ) =( 5–y ) ( y+3 )
  18. a 4 b 4 –2 a 2 b 2 –99 =( a 2 b 2 – ) ( a 2 b 2 + ) . 99 33 11 1 | 3 3 11 =( a 2 b 2 –11 ) ( a 2 b 2 +9 )
  19. c 2 +11cd+28 d 2 =( c+ ) ( c+ ) . 28 14 7 1 | 2 2 7 =( c+7d ) ( c+4d )
  20. 25 x 2 –5( 5x ) –84 =( 5x– ) ( 5x+ ) . 84 42 21 7 1 | 2 2 3 7 =( 5x–12 ) ( 5x+7 )
  21. a 2 –21ab+98 b 2 =( a– ) ( a– ) . 98 49 7 1 | 2 7 7 =( a–14b ) ( a–7b )
  22. x 4 y 4 + x 2 y 2 –132 =( x 2 y 2 + ) ( x 2 y 2 – ) . 132 66 33 11 1 | 2 2 3 11 =( x 2 y 2 +12 ) ( x 2 y 2 –11 )
  23. 48+2 x 2 – x 4 =–( x 4 –2 x 2 –48 ) =–( x 2 – ) ( x 2 + ) . 48 24 12 6 1 | 2 2 2 6 =–( x 2 –8 ) ( x 2 +6 ) =( 8– x 2 ) ( x 2 +6 )
  24. ( c+d ) 2 –18( c+d ) +65 =[ ( c+d ) – ] [ ( c+d ) – ] . 65 13 1 | 5 13 =[ ( c+d ) –5 ] [ ( c+d ) –13 ] =( c+d–5 ) ( c+d–13 )
  25. a 2 +2axy–440 x 2 y 2 =( a+ ) ( a– ) . 440 220 110 55 11 1 | 2 2 2 5 11 =( a+22xy ) ( a–20xy )
  26. m 6 n 6 –21 m 3 n 3 +104 =( m 3 n 3 – ) ( m 3 n 3 – ) . 104 52 26 13 1 | 2 2 2 13 =( m 3 n 3 –13 ) ( m 3 n 3 –8 )
  27. 14+5n– n 2 =–( n 2 –5n–14 ) =–( n– ) ( n+ ) . 14 7 1 | 2 7 =–( n–7 ) ( n+2 ) =( 7–n ) ( n+2 )
  28. x 6 + x 3 –930 =( x 3 + ) ( x 3 – ) . 930 465 155 31 1 | 2 3 5 31 =( x 3 +31 ) ( x 3 –30 )
  29. ( 4 x 2 ) 2 –8( 4 x 2 ) –105 =( 4 x 2 – ) ( 4 x 2 + ) . 105 35 7 1 | 3 5 7 =( 4 x 2 –15 ) ( 4 x 2 +7 )
  30. x 4 +5ab x 2 –36 a 2 b 2 =( x 2 + ) ( x 2 – ) . 36 18 9 1 | 2 2 9 =( x 2 +9ab ) ( x 2 –4ab )
  31. a 4 – a 2 b 2 –156 b 4 =( a 2 – ) ( a 2 + ) . 156 78 39 13 1 | 2 2 3 13 =( a 2 –13 b 2 ) ( a 2 +12 b 2 )
  32. 21 a 2 +4ax– x 2 =–( x 2 –4ax–21 a 2 ) =–( x– ) ( x+ ) . 21 7 1 | 3 7 =–( x–7a ) ( x+3a ) =( 7a–x ) ( x+3a )
  33. x 8 y 8 –15a x 4 y 4 –100 a 2 =( x 4 y 4 – ) ( x 4 y 4 + ) . 100 50 25 5 1 | 2 2 5 5 =( x 4 y 4 –20a ) ( x 4 y 4 +5a )
  34. ( a–1 ) 2 +3( a–1 ) –108 =[ ( a–1 ) + ] [ ( a–1 ) – ] . 108 54 27 9 1 | 2 2 3 9 =[ ( a–1 ) +12 ] [ ( a–1 ) –9 ] =( a–1+12 ) ( a–1–9 )
  35. m 2 +abcm–56 a 2 b 2 c 2 =( m+ ) ( m– ) . 56 28 14 7 1 | 2 2 2 7 =( m+8abc ) ( m–7abc )
  36. ( 7 x 2 ) 2 +24( 7 x 2 ) –128 =( 7 x 2 + ) ( 7 x 2 + ) . 128 64 32 16 1 | 2 2 2 16 =( 7 x 2 +16 ) ( 7 x 2 +8 )
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