By Armando Rojo
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Extra resources for Algebra II 13ed.
3 Ϫ40x6 ϭ Ί 3 ͑Ϫ8x6͒ c. Ί и5 3 ͑Ϫ2x 2͒3 ϭΊ 3 5 ϭ Ϫ2x 2 Ί Find largest cube factor. и5 Find root of perfect cube. Now try Exercise 79(b). 22 Chapter P Prerequisites Radical expressions can be combined (added or subtracted) if they are like radicals—that is, if they have the same index and radicand. For instance, Ί2, 3Ί2, and 12Ί2 are like radicals, but Ί3 and Ί2 are unlike radicals. To determine whether two radicals can be combined, you should first simplify each radical. Example 12 Combining Radicals a.
X 4͞3y 2͞3 ͑xy͒1͞3 5Ϫ1͞2 и 5x5͞2 114. ͑5x͒3͞2 In Exercises 115 and 116, reduce the index of each radical. 4 32 Ί 115. (a) 6 x3 116. (a) Ί (b) ͑x ϩ 1͒ 4 ͑3x2͒4 (b) Ί 6 Ί 4 In Exercises 117 and 118, write each expression as a single radical. Then simplify your answer. 117. (a) 118. (a) ΊΊ32 ΊΊ243͑x ϩ 1͒ (b) (b) 4 2x ΊΊ 3 10a7b ΊΊ 119. PERIOD OF A PENDULUM The period T (in seconds) of a pendulum is T ϭ 2ΊL͞32, where L is the length of the pendulum (in feet). Find the period of a pendulum whose length is 2 feet.
F ________ O ________ I ________ L ________ In Exercises 6–8, match the special product form with its name. 6. ͑u ϩ v͒͑u Ϫ v͒ ϭ u2 Ϫ v2 7. ͑u ϩ v͒2 ϭ u2 ϩ 2uv ϩ v2 8. ͑u Ϫ v͒2 ϭ u2 Ϫ 2uv ϩ v2 (a) A binomial sum squared (b) A binomial difference squared (c) The sum and difference of same terms SKILLS AND APPLICATIONS In Exercises 9–14, match the polynomial with its description. ] (a) (c) (e) 9. 10. 11. 12. 13. 14. (b) 1 Ϫ 2x3 (d) 12 2 (f) 3 x4 ϩ x2 ϩ 10 A polynomial of degree 0 A trinomial of degree 5 A binomial with leading coefficient Ϫ2 A monomial of positive degree 2 A trinomial with leading coefficient 3 A third-degree polynomial with leading coefficient 1 3x2 x3 ϩ 3x2 ϩ 3x ϩ 1 Ϫ3x5 ϩ 2x3 ϩ x In Exercises 15–18, write a polynomial that fits the description.
Algebra II 13ed. by Armando Rojo