By Raymond A. Barnett

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EXAMPLE 1 Polynomials and Nonpolynomials (A) Which of the following are polynomials? 2x ϩ 5 Ϫ 1 x x2 Ϫ 3x ϩ 2 2x3 Ϫ 4x ϩ 1 x4 ϩ 12 (B) Given the polynomial 2x3 Ϫ x6 ϩ 7, what is the degree of the first term? The third term? The whole polynomial? (C) Given the polynomial x3y2 ϩ 2x2y ϩ 1, what is the degree of the first term? The second term? The whole polynomial? SOLUTIONS MATCHED PROBLEM 1 (A) x2 Ϫ 3x ϩ 2 and x4 ϩ 12 are polynomials. ) (B) The first term has degree 3, the third term has degree 0, and the whole polynomial has degree 6.

What is the result of entering 23 on a calculator? 2 88. Refer to Problem 87. What is the difference between 2(3 ) and 3 2 32 (2 ) ? Which agrees with the value of 2 obtained with a calculator? APPLICATIONS In Problems 33–38, change to rational exponent form. Do not simplify. 33. 1361 3 34. 2 172 5 3 35. 4x 2 y 4 36. 2 7x3y2 3 2 37. 2 x ϩ y2 3 2 3 2 38. 2 x ϩ2 y In Problems 39–50, evaluate each expression that represents a real number. 39. 1001ր2 40. 1691ր2 41. 1121 42. 1361 1ր 3 44. 27 3 45. 1 Ϫ27 3 46.

The point with coordinate 0 is called the origin. The arrow on the right end of the line indicates a positive direction. The coordinates of all points to the right of the origin are called positive real numbers, and those to the left of the origin are called negative real numbers. The real number 0 is neither positive nor negative. 64 5 10 Z Figure 1 A real number line. Z Addition and Multiplication of Real Numbers How do you add or multiply two real numbers that have nonrepeating and nonterminating decimal expansions?

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