By Bernard Kolman; Arnold Shapiro

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4 FACTORING COMMON FACTORS 64 . x 2 x FIGURE 5 65. (2x + 1) (2x + 3) 69. (x + y)2 73. (2x + 1) (2x - 1) 66. (3x - 1) (x + 5) 70. (x - 4)2 74. (3a + lb)2 Now that we can find the product of two poly nomi als, let's consi der the reverse problem: gi ven a poly nomi al, can wefi nd af ctors whose product wi llyi eld the gi ven poly nomi al? Thi s process, known as factoring,i s one of the basi c tools of algebra. I n thi s chapter a poly nomi al wi th integer coeffi ci entsi s to be factored as a product of poly nomi als of lower degree wi th integer coef fici ents; a poly nomi al wi th rational coeffi ci entsi s to be factored as a product of poly nomi als of lower degree wi th rational coeffici ents.

The set of complex numbers . 49. I for the given comp lex value of x. 43. 48. -V-18 20. 2 In Exercises 35. 16. 1 9 . 0 . 3 - Y-98 _1_ _ � In Exercises 22-26 22. (x + 2) + (2y 24. - v'=36 15. KEY IDEAS FOR REVIEW 57 KEY IDEAS FOR REVIEW D A set is simply a collection of objects or numbers. D The real number system is composed of the rational and irrational numbers. The rational numbers are those that can be written as the ratio of two integers, p/q, with q '¢ O; the irrational numbers cannot be written as a ratio of integers.

X)3 42. 41 . 5 - 355 45. (x- J) - J 46. y 4 2 2x2 -J 49. 50. xy 53. ( -�x3y-4r J 54. 2b-4 57. (a2a-3c58. 3r {a + b)b}- 21 62. 61 . (a -n n 65. (�) = (�) 1 2 . -3r3r3 1 6. -(2x2)S 20. (3;:r 24. [(3b + 1 )5 ]5 28. � (y4)6 32. (xy)o 36. x- s (2a) -6 (x-2)4 48. - 1 0 x l x •2 7 ( - 2rc-2)n (x2)3(y2)4(x3)7 {-2ab2b)4 (-3a 2)3 3 ( -�a2b3c2) (-3) -3 -x- s 4y5y-2 [ (x + y) - 2]2 (x4y -2) (x-2-2)2J (3y ) ix- 3y2 x- ly- 3 (a- 1 + b- 1 ) - 1 I Show that [ill]- 68. 6s5-2· r Consider a square whose area is length a.