By Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Those authors have created a e-book to actually support scholars visualize arithmetic for larger comprehension. through growing algebraic visible side-by-sides to resolve quite a few difficulties within the examples, the authors exhibit scholars the connection of the algebraic resolution with the visible, usually graphical, answer. moreover, the authors have further quite a few new instruments to aid scholars larger use the ebook for max effectiveness not to in basic terms go the path, yet really comprehend the material.
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Extra info for Algebra and Trigonometry (3rd Edition) (Beecher/Penna/Bittinger Series)
Rationalize denominators or numerators in rational expressions. Convert between exponential and radical notation. Simplify expressions with rational exponents. A number c is said to be a square root of a if c 2 a. Thus, 3 is a square root of 9, because 32 9, and Ϫ3 is also a square root of 9, because ͑Ϫ3͒2 9. Similarly, 5 is a third root (called a cube root) of 125, because 53 125. The number 125 has no other real-number cube root. , publishing as Pearson Addison-Wesley 58. 68. ͑x ϩ 1͒ ͑x Ϫ 2͒ ͑3x Ϫ 8͒ Ϫ2x Ϫ h 2 2 73.
If there is, we factor it out first. EXAMPLE 3 Factor: x 2 ϩ 5x ϩ 6. Solution First, we look for a common factor. There is none. Next, we look for two numbers whose product is 6 and whose sum is 5. Since the constant term, 6, and the coefficient of the middle term, 5, are both positive, we look for a factorization of 6 in which both factors are positive. PAIRS OF FACTORS SUMS OF FACTORS 1, 6 7 2, 3 5 The numbers we need are 2 and 3. The factorization is ͑x ϩ 2͒ ͑x ϩ 3͒. We have x 2 ϩ 5x ϩ 6 ͑x ϩ 2͒ ͑x ϩ 3͒.
QXP 26 Chapter R 12/2/04 2:42 PM Page 26 • Basic Concepts of Algebra To factor ax 2 ϩ bx ϩ c , a 1, using the grouping method: 1. Factor out the largest common factor. 2. Multiply the leading coefficient a and the constant c. 3. Try to factor the product ac so that the sum of the factors is b. That is, find integers p and q such that pq ac and p ϩ q b. 4. Split the middle term. That is, write it as a sum using the factors found in step (3). 5. Factor by grouping. EXAMPLE 7 Factor: 12x 3 ϩ 10x 2 Ϫ 8x .
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