By ed van der Geer at al Birkhaeuser

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Extra info for Arithmetic Algebraic Geometry

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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.

TABLE 4 Number o f nth b such b "" a" roots of n b > < > < 0 O 0 0 0 that Fonn of nth Even 2 a, -a Even None None Odd Odd 1 a>O a

2x2 + 3x4 - 7x5 In Exercises 2 1-23 perfonn the indicated operations. 2 1 . (3a2b2 - a b + 2b - a) (2a2b2 + 2a1b - 2b - a) 22. x(2x - l )(x + 2) 23. 3x(2x + 1)2 - 1 perfonn the indicated operations 4 38. 2 + a-r---4 2 3 x+2 x- 1 40. + 1 4 1 . x2 + -x x - x­l 39. x2 _ _ l n Exercises simplify , and express the answers using only positive exponents. All variables are posi­ tive numbers. 42. 45. (2a2b- 3)- 3 x3 + n x" 48. v;ry 43. 2(a2 - 1 )0 46 . VsO 49. �32x8y6 44. 3 ��6r 41 2 47. V'ii Yx 50.