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 +xy12 =(xy+ ) (xy ) . 12 6 3 1 | 2 2 3 =(xy+4 ) (xy3 )
  5. (4x ) 2 2(4x ) 15 =(4x ) (4x+ ) . 15 5 1 | 3 5 =(4x5 ) (4x+3 )
  6. (5x ) 2 +13(5x ) +42 =(5x+ ) (5x+ ) . 42 21 7 1 | 2 3 7 =(5x+6 ) (5x+7 )
  7. x 2 +2ax15 a 2 =(x+ ) (x ) . 15 5 1 | 3 5 =(x+5a ) (x3a )
  8. a 2 4ab21 b 2 =(a ) (a+ ) . 21 7 1 | 3 7 =(7a7b ) (7a+3b )
  9. (xy ) 2 +2(xy ) 24 =[(xy ) + ] [(xy ) ] . 24 12 6 1 | 2 2 6 =[(xy ) +6 ] [(xy ) 4 ] =(xy+6 ) (xy4 )
  10. 5+4x x 2 =( x 2 4x5 ) =(x ) (x+ ) . 5 1 | 5 =(x5 ) (x+1 ) =(5x ) (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 +mn56 n 2 =(m+ ) (m ) . 56 28 14 7 1 | 2 2 2 7 =(m+8n ) (m7n )
  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 =(2x3 ) (2x1 )
  15. (mn ) 2 +5(mn ) 24 =[(mn ) + ] [(mn ) ] . 24 12 6 3 1 | 2 2 2 3 =[(mn ) +8 ] [(mn ) 3 ] =(mn+8 ) (mn3 )
  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 2y15 ) =(y ) (y+ ) . 15 5 1 | 3 5 =(y5 ) (y+3 ) =(5y ) (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 =(5x12 ) (5x+7 )
  21. a 2 21ab+98 b 2 =(a ) (a ) . 98 49 7 1 | 2 7 7 =(a14b ) (a7b )
  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+d5 ) (c+d13 )
  25. a 2 +2axy440 x 2 y 2 =(a+ ) (a ) . 440 220 110 55 11 1 | 2 2 2 5 11 =(a+22xy ) (a20xy )
  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 5n14 ) =(n ) (n+ ) . 14 7 1 | 2 7 =(n7 ) (n+2 ) =(7n ) (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 4ax21 a 2 ) =(x ) (x+ ) . 21 7 1 | 3 7 =(x7a ) (x+3a ) =(7ax ) (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. (a1 ) 2 +3(a1 ) 108 =[(a1 ) + ] [(a1 ) ] . 108 54 27 9 1 | 2 2 3 9 =[(a1 ) +12 ] [(a1 ) 9 ] =(a1+12 ) (a19 )
  35. m 2 +abcm56 a 2 b 2 c 2 =(m+ ) (m ) . 56 28 14 7 1 | 2 2 2 7 =(m+8abc ) (m7abc )
  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 )