By Ron Larson
ALGEBRA AND TRIGONOMETRY: genuine arithmetic, actual humans, seventh variation, is a perfect scholar and teacher source for classes that require using a graphing calculator. the standard and volume of the workouts, mixed with fascinating functions and leading edge assets, make educating more straightforward and aid scholars be successful. keeping the sequence’ emphasis on scholar help, chosen examples through the textual content comprise notations directing scholars to earlier sections to check ideas and talents had to grasp the fabric handy. The ebook additionally achieves accessibility via cautious writing and design—including examples with certain strategies that commence and finish at the comparable web page, which maximizes clarity. equally, side-by-side recommendations convey algebraic, graphical, and numerical representations of the maths and aid quite a few studying types. 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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Additional resources for Algebra and Trigonometry: Real Mathematics Real People
17(7 ∙ 12) = (17 ∙ 7)12 = 1 ∙ 12 = 12 115. 117. 1 1 > , where a ≠ 0 and b ≠ 0. a b 130. Think About It (a) Use a calculator to complete the table. (b) x = −4 Identifying Rules of Algebra In Exercises 109–114, identify the rule(s) of algebra illustrated by the statement. 11 Real Numbers (b) −C C (c) B − A (d) A − C HOW DO YOU SEE IT? Match each description with its graph. 1 on page 2 may be included in a range of prices? a range of lengths? Explain. 90. 03 centimeter. 133. Think About It Describe the real number values of u and v for which u + v is greater than, less than, and equal to u + v .
Divide out common factors. Note that the original expression is undefined when x = 2 (because division by zero is undefined). To make the simplified expression equivalent to the original expression, you must restrict the domain of the simplified expression by excluding the value x = 2. com. 4x + 12 in simplest form. x2 − 3x − 18 It may sometimes be necessary to change the sign of a factor by factoring out (−1) to simplify a rational expression, as shown in Example 3. E XAM P L E 3 Simplifying a Rational Expression 12 + x − x2 (4 − x)(3 + x) = 2 2x − 9x + 4 (2x − 1)(x − 4) = − (x − 4)(3 + x) (2x − 1)(x − 4) =− Checkpoint Write 3+x , 2x − 1 x≠4 Factor completely.
Factoring Special Polynomial Forms Factored Form Difference of Two Squares u2 − v2 = (u + v)(u − v) Example 9x 2 − 4 = (3x)2 − 22 = (3x + 2)(3x − 2) Perfect Square Trinomial u2 + 2uv + v2 = (u + v)2 x 2 + 6x + 9 = x 2 + 2(x)(3) + 32 = (x + 3)2 u2 − 2uv + v2 = (u − v)2 x 2 − 6x + 9 = x 2 − 2(x)(3) + 32 = (x − 3)2 Sum or Difference of Two Cubes u3 + v3 = (u + v)(u2 − uv + v2) x 3 + 8 = x 3 + 23 = (x + 2)(x 2 − 2x + 4) u3 − v3 = (u − v)(u2 + uv + v2) 27x 3 − 1 = (3x)3 − 13 = (3x − 1)(9x 2 + 3x + 1) For the difference of two squares, you can think of this form as follows.