By Ron Larson, Robert P. Hostetler
This market-leading textual content maintains to supply scholars and teachers with sound, always established reasons of the mathematical ideas. Designed for a two-term direction, the hot 7th variation keeps the gains that experience made Algebra and Trigonometry a whole resolution for either scholars and teachers: fascinating purposes, state of the art layout, and cutting edge expertise mixed with an abundance of conscientiously written workouts.
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Extra resources for Algebra and Trigonometry (7th Edition)
Factor according to one of the special polynomial forms. 3. Factor as ax2 ϩ bx ϩ c ϭ ͑mx ϩ r͒͑nx ϩ s͒. 4. Factor by grouping. com for worked-out solutions to odd-numbered exercises. VOCABULARY In Exercises 1–3, fill in the blanks. 1. The process of writing a polynomial as a product is called ________. 2. A polynomial is ________ ________ when each of its factors is prime. 3. If a polynomial has more than three terms, a method of factoring called ________ ________ ________ may be used. 4. Match the factored form of the polynomial with its name.
5 2Ί3 b. 2 3 Ί 5 Solution a. b. 5 2Ί3 2 3 5 Ί ϭ Ί3 5 2Ί3 иΊ 3 Ί3 is rationalizing factor. ϭ 5Ί3 2͑3͒ Multiply. ϭ 5Ί3 6 Simplify. ϭ 2 3 5 Ί 3 52 Ί иΊ 3 52 3 52 is rationalizing factor. Ί ϭ 3 52 2Ί 3 Ί53 Multiply. ϭ 3 25 2Ί 5 Simplify. Now try Exercise 95. 2 Example 14 ϭ 23 Rationalizing a Denominator with Two Terms 2 2 ϭ 3 ϩ Ί7 3 ϩ Ί7 ϭ Exponents and Radicals и Multiply numerator and denominator by conjugate of denominator. 3 Ϫ Ί7 3 Ϫ Ί7 2͑3 Ϫ Ί7 ͒ 3͑3͒ ϩ 3͑ϪΊ7 ͒ ϩ Ί7͑3͒ Ϫ ͑Ί7 ͒͑Ί7 ͒ 2͑3 Ϫ Ί7 ͒ ͑3͒2 Ϫ ͑Ί7 ͒2 Use Distributive Property.
Example 9 Factoring by Grouping Use factoring by grouping to factor x 3 Ϫ 2x 2 Ϫ 3x ϩ 6. Another way to factor the polynomial in Example 9 is to group the terms as follows. x3 Ϫ 2x2 ϭ͑ x3 Ϫ 3x͒ Ϫ ͑ ϭ x͑ Ϫ 3͒ Ϫ 2͑ ϭ͑ Ϫ 3͒͑x Ϫ 2͒ x2 x 3 Ϫ 2x 2 Ϫ 3x ϩ 6 ϭ ͑x 3 Ϫ 2x 2͒ Ϫ ͑3x Ϫ 6͒ Ϫ 3x ϩ 6 2x2 x2 Solution x2 Ϫ 6͒ Ϫ 3͒ As you can see, you obtain the same result as in Example 9. Group terms. ϭ x 2͑x Ϫ 2͒ Ϫ 3͑x Ϫ 2͒ Factor each group. ϭ ͑x Ϫ 2͒͑x 2 Ϫ 3͒ Distributive Property Now try Exercise 73. Factoring a trinomial can involve quite a bit of trial and error.