By Crossley J.N. (ed.)
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Extra resources for Algebra and logic: Proceedings Clayton, 1974
Express your answer in scientiﬁc notation. 93. 92. Repeat Exercise 88 and conﬁrm your answer with a calculator. 94. 3 Page 28 P O LY N O M I A L S : B A S I C O P E R AT I O N S S K I LLS O BJ E CTIVE S ■ ■ ■ C O N C E P TUAL O BJ E CTIVE S Add and subtract polynomials. Multiply polynomials. Recognize special products. ■ ■ Recognize like terms. Learn formulas for special products. Adding and Subtracting Polynomials Polynomials in Standard Form The expressions 3x2 Ϫ 7x Ϫ 1 4y3 Ϫ y 5z are all examples of polynomials in one variable.
4-3 # 1 1 33 = 1 , a 3b = 1 # = 33 = 27 1 1 3 a 3b 3 1 1 16 = 3 # 24 = = 64 2-4 4 d. - 23 # 1 4 1 = - 23 # (- 6)2 = (- 8)(36) = (-6)-2 Ϫ8 36 ■ YO U R T U R N u b. qxd Evaluate the expressions. a. - 1 5-2 b. 1 # -2 6 3-2 - 288 ■ Answer: a. Ϫ25 b. qxd 8/7/12 20 5:34 PM Page 20 C H A P T E R 0 Prerequisites and Review Now we can evaluate expressions involving positive and negative exponents. How do we evaluate an expression with a zero exponent? We deﬁne any nonzero real number raised to the zero power as 1.
A) ϭ a Ϫ(Ϫ9) ϭ 9 A negative sign preceding an expression is distributed throughout the expression. Ϫ(a ϩ b) ϭ Ϫa Ϫ b Ϫ(a Ϫ b) ϭ Ϫa ϩ b Ϫ3(x ϩ 5) ϭ Ϫ3x Ϫ 15 Ϫ3(x Ϫ 5) ϭ Ϫ3x ϩ 15 EXAMPLE 8 or or Using Properties of Negatives Eliminate the parentheses and perform the operations. a. Ϫ5 ϩ 7 Ϫ (Ϫ2) b. Ϫ(Ϫ3)(Ϫ4)(Ϫ6) Technology Tip a. Solution: a. Distribute the negative. qxd ϩ2 ϭ Ϫ5 ϩ 7 ϩ 2 Combine the three quantities. b. Group the terms. ϭ 4 [Ϫ(Ϫ3)][(Ϫ4)(Ϫ6)] Perform the multiplication inside the [ ].
Algebra and logic: Proceedings Clayton, 1974 by Crossley J.N. (ed.)