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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 +5ax–21 =6 a 2 x 2 –9ax+14ax–21 . 126 63 21 7 1 | 2 3 3 7 =3ax( 2ax–3 ) +7( 2ax–3 ) =( 2ax–3 ) ( 3ax+7 )
  5. 20 x 2 y 2 +9xy–20 =20 x 2 y 2 +25xy–16xy–20 . 400 200 100 50 25 1 | 2 2 2 2 25 =5xy( 4xy+5 ) –4( 4xy+5 ) =( 4xy+5 ) ( 5xy–4 )
  6. 15 x 2 –ax–2 a 2 =15 x 2 +5ax–6ax–2 a 2 . 30 15 5 1 | 2 3 5 =5x( 3x+a ) –2a( 3x+a ) =( 3x+a ) ( 5x–2a )
  7. 12–7x–10 x 2 =12+8x–15x–10 x 2 . 120 60 30 15 1 | 2 2 2 15 =4( 3+2x ) –5x( 3+2x ) =( 3+2x ) ( 4–5x )
  8. 21 x 2 –29xy–72 y 2 =21 x 2 –56xy+27xy–72 y 2 . 1512 756 378 189 63 21 7 1 | 2 2 2 3 3 3 7 =7x( 3x–8y ) –9y( 3x–8y ) =( 3x–8y ) ( 7x–9y )
  9. 6 m 2 –13am–15 a 2 =6 m 2 –18am+5am–15 a 2 . 90 45 15 5 1 | 2 3 3 5 =6m( m–3a ) –5a( m–3a ) =( m–3a ) ( 6m–5a )
  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 –13ab–3 b 2 =30 a 2 +5ab–18ab–3 b 2 . 90 45 15 5 1 | 2 3 3 5 =5a( 6a+b ) –3b( 6a+b ) =( 6a+b ) ( 5a–3b )
  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+13a–3 a 2 =30–5a+18a–3 a 2 . 90 45 15 5 1 | 2 3 3 5 =5( 6–a ) –3a( 6–a ) =( 6–a ) ( 5–3a )
  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 ) ( 5–3 x 4 )
  15. 6 a 2 –ax–15 x 2 =6 a 2 +9ax–10ax–15 x 2 . 90 45 15 5 1 | 2 3 3 5 =3a( 2a+3x ) –5x( 2a+3x ) =( 2a+3x ) ( 3a–5 )
  16. 4 x 2 +7mnx–15 m 2 n 2 =4 x 2 +12mnx–5mnx–15 m 2 n 2 . 60 30 15 5 1 | 2 2 3 5 =4x( x+3mn ) –5mn( x+3mn ) =( x+3mn ) ( 4x–5mn )
  17. 18 a 2 +17ay–15 y 2 =18 a 2 +27ay–10ay–15 y 2 . 270 135 45 15 5 1 | 2 3 3 3 5 =9a( 2a+3y ) –5y( 2a+3y ) =( 2a+3y ) ( 9a–5 )
  18. 15+2 x 2 –8 x 4 =15–10 x 2 +12 x 2 –8 x 4 . 120 60 30 15 5 1 | 2 2 2 3 5 =5( 3–2 x 2 ) +4 x 2 ( 3–2 x 2 ) =( 3–2 x 2 ) ( 5+4 x 2 )
  19. 6–25 x 8 +5 x 4 =6+5 x 4 –25 x 8 =6–10 x 4 +15 x 4 –25 x 8 . 150 75 25 5 1 | 2 3 5 5 =2( 3–5 x 4 ) +5 x 4 ( 3–5 x 4 ) =( 3–5 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 +17am–21 a 2 =30 m 2 +35am–18am–21 a 2 . 630 315 105 35 1 | 2 3 3 35 =5m( 6m+7a ) –3a( 6m+7a ) =( 6m+7a ) ( 5m–3a )
  22. 16a–4–15 a 2 =–( 15 a 2 –16a+4 ) . 60 30 15 5 1 | 2 2 3 5 =–( 15 a 2 –10a–6a+4 ) =–[ 5a( 3a–2 ) –2( 3a–2 ) ] =–( 3a–2 ) ( 5a–2 ) =( 2–3a ) ( 5a–2 )
  23. 11xy–6 y 2 –4 x 2 =–( 4 x 2 –11xy+6 y 2 ) . 24 12 6 3 1 | 2 2 2 3 =–( 4 x 2 –8xy–3xy+6 y 2 ) =–[ 4x( x–2y ) –3y( x–2y ) ] =–( x–2y ) ( 4x–3y ) =( 2y–x ) ( 4x–3y )
  24. 27ab–9 b 2 –20 a 2 =–( 20 a 2 –27ab+9 b 2 ) . 180 90 45 15 1 | 2 2 3 15 =–( 20 a 2 –15ab–12ab+9 b 2 ) =–[ 5a( 4a–3b ) –3b( 4a–3b ) ] =–( 4a–3b ) ( 5a–3b ) =( 3b–4a ) ( 5a–3b )
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