Algebra and Trigonometry (Eighth Edition) by Ron Larson

By Ron Larson

This market-leading textual content keeps to supply scholars and teachers with sound, regularly dependent motives of the mathematical ideas. Designed for a two-term direction, the hot 8th version keeps the positive aspects that experience made Algebra and Trigonometry a whole resolution for either scholars and teachers: fascinating functions, state of the art layout, and cutting edge expertise mixed with an abundance of conscientiously written routines.

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X 2 Ϫ 10x ϩ 25 ϭ x 2 Ϫ 2͑x͒͑5͒ ϩ 5 2 ϭ ͑x Ϫ 5͒2 b. 16x2 ϩ 24x ϩ 9 ϭ ͑4x͒2 ϩ 2͑4x͒͑3͒ ϩ 32 ϭ ͑4x ϩ 3͒2 Now try Exercise 35. The next two formulas show the sums and differences of cubes. Pay special attention to the signs of the terms. Like signs Like signs u 3 ϩ v 3 ϭ ͑u ϩ v͒͑u 2 Ϫ uv ϩ v 2͒ u 3 Ϫ v 3 ϭ ͑u Ϫ v͒͑u 2 ϩ uv ϩ v 2͒ Unlike signs Example 5 Unlike signs Factoring the Difference of Cubes Factor x 3 Ϫ 27. Solution x3 Ϫ 27 ϭ x3 Ϫ 33 ϭ ͑x Ϫ 3͒͑x 2 ϩ 3x ϩ 9͒ Rewrite 27 as 33. Factor. Now try Exercise 45.

Some numbers have more than one nth root. For example, both 5 and Ϫ5 are square roots of 25. The principal square root of 25, written as Ί25, is the positive root, 5. The principal nth root of a number is defined as follows. Principal nth Root of a Number Let a be a real number that has at least one nth root. The principal nth root of a is the nth root that has the same sign as a. It is denoted by a radical symbol n a. Ί Principal nth root The positive integer n is the index of the radical, and the number a is the radicand.

For instance, a factoring model for 2 x 2 ؉ 3x ؉ 1 ‫ͧ ؍‬2 x ؉ 1ͨͧx ؉ 1ͨ 43 Factoring Polynomials r 44 131. Chapter P x 8 x x x Prerequisites 132. x 3 x x x x+3 18 4 5 5 (x 4 + 3) In Exercises 133–138, completely factor the expression. 133. 134. 135. 136. x4͑4͒͑2x ϩ 1͒3͑2x͒ ϩ ͑2x ϩ 1͒4͑4x3͒ x3͑3͒͑x2 ϩ 1͒2͑2x͒ ϩ ͑x2 ϩ 1͒3͑3x2͒ ͑2x Ϫ 5͒4͑3͒͑5x Ϫ 4͒2͑5͒ ϩ ͑5x Ϫ 4͒3͑4͒͑2x Ϫ 5͒3͑2͒ ͑x2 Ϫ 5͒3͑2͒͑4x ϩ 3͒͑4͒ ϩ ͑4x ϩ 3͒2͑3͒͑x2 Ϫ 5͒2͑x2͒ 137. ͑5x Ϫ 1͒͑3͒ Ϫ ͑3x ϩ 1͒͑5͒ ͑5x Ϫ 1͒2 138. ͑2x ϩ 3͒͑4͒ Ϫ ͑4x Ϫ 1͒͑2͒ ͑2x ϩ 3͒2 In Exercises 139–142, find all values of b for which the trinomial can be factored.

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