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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 )
Categories: Capítulo X