# Algebra and Trigonometry: Real Mathematics Real People by Ron Larson

By Ron Larson

ALGEBRA AND TRIGONOMETRY: genuine arithmetic, genuine humans, seventh version, is a perfect pupil and teacher source for classes that require using a graphing calculator. the standard and volume of the workouts, mixed with attention-grabbing purposes and cutting edge assets, make educating more straightforward and support scholars be successful. preserving the sequence’ emphasis on scholar help, chosen examples through the textual content contain notations directing scholars to prior sections to check ideas and abilities had to grasp the fabric handy. The publication additionally achieves accessibility via cautious writing and design—including examples with certain suggestions that start and finish at the similar web page, which maximizes clarity. equally, side-by-side suggestions convey algebraic, graphical, and numerical representations of the math and help quite a few studying kinds. Reflecting its subtitle, this crucial revision focuses greater than ever on displaying scholars the relevance of arithmetic of their lives and destiny careers.

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Extra resources for Algebra and Trigonometry: Real Mathematics Real People

Sample text

Com. Factor 64x3 − 1. E XAM P L E 11 Factoring the Sum of Cubes a. y3 + 125 = y3 + 53 Rewrite 125 as 53. = ( y + 5)(y2 − 5y + 25) b. 3x3 + 192 = 3( x3 + 64) 3 is a common factor. = 3(x3 + 43) Rewrite 64 as 43. = 3(x + 4)(x2 − 4x + 16) Factor. Checkpoint Factor each expression. a. x 3 + 216 b. 5y 3 + 135 Factor. com. Rewrite u6 − v6 as the difference of two squares. Then find a formula for completely factoring u6 − v6. Use your formula to factor completely x6 − 1 and x6 − 64. 3 Polynomials and Factoring Trinomials with Binomial Factors To factor a trinomial of the form ax2 + bx + c, use the following pattern.

3x2 + 10x + 8 143. 3t 3 + 24 144. 4x 3 − 32 145. 4x(2x − 1) + 2(2x − 1)2 146. 5(3 − 4x)2 − 8(3 − 4x)(5x − 1) 147. 2(x + 1)(x − 3)2 − 3(x + 1)2(x − 3) 148. 7(3x + 2)2(1 − x)2 + (3x + 2)(1 − x)3 149. MODELING DATA After 2 years, an investment of \$1000 compounded annually at an interest rate r (in decimal form) will yield an amount of 1000(1 + r)2. (a) Write this polynomial in standard form. (b) Use a calculator to evaluate the polynomial for the values of r shown in the table. 1% 112% r 2% 212% 3% 1000(1 + r)2 (c) What conclusion can you make from the table?

6. For n even, √ For n odd, ∙ √7 = √5 ∙ 7 = √35 4 27 √ a , b≠0 b )2 = (2)2 = 4 n an √ = a. ∣ ∣ √(−12)2 = −12 = 12 3 √ (−12) = −12 3 A common special case of Property 6 is ∣∣ √a2 = a . E XAM P L E 8 Using Properties of Radicals Use the properties of radicals to simplify each expression. 3 5 b. (√ ) 3 a. √8 ∙ √2 3 3 c. √ x 6 6 d. √ y Solution a. b. c. d. com. Use the properties of radicals to simplify each expression. a. √125 √5 3 b. com 3 2 √ c. √ x ∙ 3x d. √ √x Technology Tip There are three methods of evaluating radicals on most graphing calculators.