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Atomic theory;: An elementary exposition by Arthur Haas

By Arthur Haas

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Evaluate Evaluate · when - 1, Graph the inequality 1 � < Graph the inequality � � I, an integer. 15. Give the inequality represented on the following number line. 45, � 2'1,1' -0 4 -5 2m3m -5n m = 2, n = 4. -n x2x+-y2y x = 3, y -5. -2[(p -2q)p· q-2r - p)] p = 2, q = -3, r = -2. 2a ) 3( 1 -1 _3141-1+41 _-721 1 . PROGRESS TEST lB 2. 3. 4. 5. l. The numbers are (a) integers (b) irrational numbers (d) none of these. (c) rational numbers The numbers - Y7. 9 are (a) natural numbers (b) irrational numbers (d) none of these.

Graph the inequality -2 < x � 5. 14. Graph the inequality -5 � x � - 1, x an integer. 15. Give the inequality represented on the following number line. -3 - 2 -] 0 2 3 39 CHAPTER TWO POLYNOMIALS Polynomials play an important role in the study of algebra since many word problems translate into equations or inequalities that involve polynomials. We first study the manipulative and mechanical aspects of polynomials; this will serve as background for dealing with their applications in later chapters.

3ab2)(2ab) 5. 2x(x2 + 3x - 5) 7. -2s3(2st2 - 2st + 6) 9. 4a2b2(2a2 + ab - b2 ) l l . (x + 2)(x - 3) 13. (y + 5)(y + 2) 15. (x + 3)2 2. (6x2)( -5x4) 4. ( -3s2t)(4s) 6. 8. 10. 12. 14. 16. 6x2(2x3 - 2x2 + 5) a3( -3a2 - a + 2) 4y(2y3 - 3y + 3) (x - l)(x + 4) (a - 3)(a - 4) (y - 2)(y - 2) Perform the indicated multiplication mentally in each of the following. 17. 19. 21. 23. (s + 3)(s - 3) (3x + 2)(x l ) (a - 2)(2a + 5) (2y + 3)(3y + 2) - 18. 20. 22. 24. (t + 6)(1 - 6) (2x - 3)(x + l ) (a + 3)(3a - 2) (3x - 2)(2x + 3) 55 56 POLYNOMIALS 25.

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