Ejercicio 101

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CAPITULO X

Descomposición Factorial
Ejercicio 101
Factorar:
  1. 6 x 4 +5 x 2 6 =6 x 4 +9 x 2 4 x 2 6 . 36 18 9 1 | 2 2 9 =3 x 2 (2 x 2 +3 ) 2(2 x 2 +3 ) =(2 x 2 +3 ) (3 x 2 2 )
  2. 5 x 6 +4 x 3 12 =5 x 6 +10 x 3 6 x 3 12 . 60 30 15 5 1 | 2 2 3 5 =5 x 3 ( x 3 +2 ) 6( x 3 +2 ) =( x 3 +2 ) (5 x 3 6 )
  3. 10 x 8 +29 x 4 +10 =10 x 8 +25 x 4 +4 x 4 +10 . 100 50 25 1 | 2 2 25 =5 x 4 (2 x 2 +5 ) +2(2 x 2 +5 ) =(2 x 2 +5 ) (5 x 5 +2 )
  4. 6 a 2 x 2 +5ax21 =6 a 2 x 2 9ax+14ax21 . 126 63 21 7 1 | 2 3 3 7 =3ax(2ax3 ) +7(2ax3 ) =(2ax3 ) (3ax+7 )
  5. 20 x 2 y 2 +9xy20 =20 x 2 y 2 +25xy16xy20 . 400 200 100 50 25 1 | 2 2 2 2 25 =5xy(4xy+5 ) 4(4xy+5 ) =(4xy+5 ) (5xy4 )
  6. 15 x 2 ax2 a 2 =15 x 2 +5ax6ax2 a 2 . 30 15 5 1 | 2 3 5 =5x(3x+a ) 2a(3x+a ) =(3x+a ) (5x2a )
  7. 127x10 x 2 =12+8x15x10 x 2 . 120 60 30 15 1 | 2 2 2 15 =4(3+2x ) 5x(3+2x ) =(3+2x ) (45x )
  8. 21 x 2 29xy72 y 2 =21 x 2 56xy+27xy72 y 2 . 1512 756 378 189 63 21 7 1 | 2 2 2 3 3 3 7 =7x(3x8y ) 9y(3x8y ) =(3x8y ) (7x9y )
  9. 6 m 2 13am15 a 2 =6 m 2 18am+5am15 a 2 . 90 45 15 5 1 | 2 3 3 5 =6m(m3a ) 5a(m3a ) =(m3a ) (6m5a )
  10. 14 x 4 45 x 2 14 =14 x 4 49 x 2 +4 x 2 14 . 196 98 49 1 | 2 2 49 =7 x 2 (2 x 2 7 ) 2(2 x 2 7 ) =(2 x 2 7 ) (7 x 2 2 )
  11. 30 a 2 13ab3 b 2 =30 a 2 +5ab18ab3 b 2 . 90 45 15 5 1 | 2 3 3 5 =5a(6a+b ) 3b(6a+b ) =(6a+b ) (5a3b )
  12. 7 x 6 33 x 3 10 =7 x 6 35 x 3 +2 x 3 10 . 70 35 1 | 2 35 =7 x 3 ( x 3 5 ) 2( x 3 5 ) =( x 3 5 ) (7 x 3 2 )
  13. 30+13a3 a 2 =305a+18a3 a 2 . 90 45 15 5 1 | 2 3 3 5 =5(6a ) 3a(6a ) =(6a ) (53a )
  14. 5+7 x 4 6 x 8 =5+10 x 4 3 x 4 6 x 8 . 30 15 5 1 | 2 3 5 =5(1+2 x 4 ) 3 x 4 (1+2 x 4 ) =(1+2 x 4 ) (53 x 4 )
  15. 6 a 2 ax15 x 2 =6 a 2 +9ax10ax15 x 2 . 90 45 15 5 1 | 2 3 3 5 =3a(2a+3x ) 5x(2a+3x ) =(2a+3x ) (3a5 )
  16. 4 x 2 +7mnx15 m 2 n 2 =4 x 2 +12mnx5mnx15 m 2 n 2 . 60 30 15 5 1 | 2 2 3 5 =4x(x+3mn ) 5mn(x+3mn ) =(x+3mn ) (4x5mn )
  17. 18 a 2 +17ay15 y 2 =18 a 2 +27ay10ay15 y 2 . 270 135 45 15 5 1 | 2 3 3 3 5 =9a(2a+3y ) 5y(2a+3y ) =(2a+3y ) (9a5 )
  18. 15+2 x 2 8 x 4 =1510 x 2 +12 x 2 8 x 4 . 120 60 30 15 5 1 | 2 2 2 3 5 =5(32 x 2 ) +4 x 2 (32 x 2 ) =(32 x 2 ) (5+4 x 2 )
  19. 625 x 8 +5 x 4 =6+5 x 4 25 x 8 =610 x 4 +15 x 4 25 x 8 . 150 75 25 5 1 | 2 3 5 5 =2(35 x 4 ) +5 x 4 (35 x 4 ) =(35 x 4 ) (2+5 x 4 )
  20. 30 x 10 91 x 5 30 =30 x 10 +100 x 5 9 x 5 30 . 900 450 225 75 25 5 1 | 2 2 3 3 5 5 =10 x 5 (3 x 5 10 ) 3(3 x 5 10 ) =(3 x 5 10 ) (10 x 5 3 )
  21. 30 m 2 +17am21 a 2 =30 m 2 +35am18am21 a 2 . 630 315 105 35 1 | 2 3 3 35 =5m(6m+7a ) 3a(6m+7a ) =(6m+7a ) (5m3a )
  22. 16a415 a 2 =(15 a 2 16a+4 ) . 60 30 15 5 1 | 2 2 3 5 =(15 a 2 10a6a+4 ) =[5a(3a2 ) 2(3a2 ) ] =(3a2 ) (5a2 ) =(23a ) (5a2 )
  23. 11xy6 y 2 4 x 2 =(4 x 2 11xy+6 y 2 ) . 24 12 6 3 1 | 2 2 2 3 =(4 x 2 8xy3xy+6 y 2 ) =[4x(x2y ) 3y(x2y ) ] =(x2y ) (4x3y ) =(2yx ) (4x3y )
  24. 27ab9 b 2 20 a 2 =(20 a 2 27ab+9 b 2 ) . 180 90 45 15 1 | 2 2 3 15 =(20 a 2 15ab12ab+9 b 2 ) =[5a(4a3b ) 3b(4a3b ) ] =(4a3b ) (5a3b ) =(3b4a ) (5a3b )