New PDF release: Amsco's Algebra Two and Trigonometry

By Gantert

ISBN-10: 1567657036

ISBN-13: 9781567657036

Algebra 2 trigonometry textbook will educate scholars every thing there's to grasp made effortless!

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Extra info for Amsco's Algebra Two and Trigonometry

Example text

The least common denominator is the product of all of the factors of the first denominator times all factors of the second that are not factors of the first. Then multiply each fraction by a fraction equal to 1 so that the denominator of each fraction will be equal to the LCD. Factors of 2a 1 2: 2 ؒ (a 1 1) (a 1 1) ؒ (a 2 1) Factors of a2 2 1: LCD: 2 ؒ (a 1 1) ؒ (a 2 1) 1 2a 1 2 1 5 2(a 11 1) ? aa 2 2 1 and 1 a2 2 1 2 1 5 2(a 1a 1)(a 2 1) 1 2 5 (a 1 1)(a 2 1) ? 2 2 5 2(a 1 1)(a 2 1) a 2 1 1 2 a 1 1 1 1 a2 2 1 5 2(a 1 1)(a 2 1) 5 2(a 1 1)(a 2 1) Since this sum has a common factor in the numerator and denominator, it can be reduced to lowest terms.

A quadratic inequality in which the product of two linear factors is less than zero is also solved by considering two cases. A product is negative if the two factors have opposite signs. Therefore, we must consider the case in which the first factor is positive and the second factor is negative and the case in which the first factor is negative and the second factor is positive. pgs 8/12/08 32 1:47 PM Page 32 The Integers Procedure 1 To solve a quadratic inequality: CASE 1 The quadratic inequality is of the form (x 2 a)(x 2 b) .

For instance: 1 5 • x 2x has no meaning when x 5 0. 2 2 1 • a 4ab has no meaning when a 5 0 or when b 5 0. y 2 2 y 2 2 • y2 2 5y 1 6 5 (y 2 2)(y 2 3) has no meaning when y 5 2 or when y 5 3. EXAMPLE 1 2 5 For what value or values of a is the fraction 3a2 2a 2 4a 1 1 undefined? Solution A fraction is undefined or has no meaning when a factor of the denominator is equal to 0. How to Proceed 3a2 2 4a 1 1 5 (3a 2 1)(a 2 1) (1) Factor the denominator: (2) Set each factor equal to 0: 3a 2 1 5 0 a2150 (3) Solve each equation for a: 3a 5 1 a51 a5 1 3 Answer The fraction is undefined when a 5 13 and when a 5 1.

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Amsco's Algebra Two and Trigonometry by Gantert


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