Ingenierias

EJERCICIOS DE CASOS DE FACTORIZACIÓN

PRESENTADO POR:
LUIS CORONADO CASTRILLÓN
LEONARDO DIAZ RODRIGUEZ
JUDITH MENDOZA ESTRADA
JASIBIS PERTUZ QUESADA
LILIANA TERAN ARGOTA

PRESENTADO A:ELIAS CASTRO MATTOS

UNIVERSIDAD SIMÓN BOLÍVAR
FACULTAD DE INGENIERÍA
INGENIERIA INDUSTRIAL
BARRANQUILLA
2012
EJERCICIOS PARES

2. m2 + 2mx + x2
= (m + x)2 R/
4. x2 – 36
= (x + 6) (x -6) R/
6. x2 – 3x – 4
= (x – 4) (x + 1) R/
8. 1 + x3
= (1 + x) (1 – x + x2) R/
10. x5 + m5
= (x + m) (x4 – mx3 + m2x2 + m3x + m4) R/

12. 2xy – 6y + xz – 3z
= (2xy – 6y) + (xz – 3z)
=2y(x – 3) + z(x – 3)
= (x - 3) (2y + z) R/

14. 4x4 + 3x2y2 + y4
= 4x4 + 4x2y2 + y4 – x2y2
= (4x4 + 4x2y2 + y4) – x2y2
= (2x2 + y2)2 – (xy)2
= (2x2 + y2 + xy) (2x2 + y2 – xy)
= (2x2 + xy +y2) (2x2 – xy + y2) R/

16. a2 – a – 30
= (a - 6) (a + 5) R/

18. a6+ 1 = (a2)3 + 1
= (a2 + 1) [(a2)2 – a2(1) + (1)2]
= (a2 + 1) (a4 – a2 + 1) R/
20. 16a2 – 24ab + 9b2
= (4a – 3b)2 R/22. 8a3 – 12a2 + 6a - 1
= (2a)3 – 3(2a)2 + 3(2a) – 13
= (2a – 1)3 R/

24. x4 + 4x2 – 21
= (x2 + 7) (x2 – 3) R/

26. a2 + 2ab + b2 – m2
= (a + b)2 – m2
= (a + b+ m) (a + b – m) R/28. x5 – x4 + x – 1
= (x5 – x4) + (x – 1)
= x4(x – 1) + (x – 1)
= (x – 1) (x4 + 1) R/

30. 25x4 – 81y2
= (5x2)2 – (9y)2
= (5x2 + 9y) (5x2 – 9y) R/

32. x2 – a2 + 2xy + y2 + 2ab – b2= (x2 + 2xy + y2) + [(-a)2 + 2ab – b2)
= (x2 + 2xy + y2 ) – (a2 – 2ab + b2)
= (x + y)2 – (a – b)2
= [x + y + (a – b)] [x + y – (a – b)]
= (x + y +a – b) (x + y – a + b) R/

34. a(x + 1) –b(x + 1) + c(x + 1)
= (x + 1) (a – b + c) R/

36. 1 – a2b4
= 1 – (ab2)2
= (1 + ab2) (1 – ab2) R/

38. x6 + 4x3 – 77
= (x3 + 11) (x3 – 7) R/

40. 1+ (a – 3b)3
= [ 1+ (a – 3b)] [1 –(a – 3b) + (a – 3b)2]
= (1 + a – 3b) (1 – a + 3b + a2 – 6ab + 9b2) R/

42. a8 – 28a4 + 36
= a8 – 12a4 – 16a4 + 36
= (a8 – 12a4 + 36) – 16a4 = (a4 – 6)2 – 16a4
= (a4 – 6 – 4a2) (a4 – 6 +...