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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 )
Categories: Capítulo X