By Margaret Lial, Ray Greenwell, Nathan Ritchey
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Here 21 / 2 , 1 / 2, so the common factor is 2 1 3x 2 1 2 21/2 and the factored form is 2 1 3x 2 1 2 21/2 3 1 x2 1 5 2 1 1 3x 2 1 2 x 4 5 2 1 3x 2 1 2 21/2 1 4x 2 2 x 1 5 2 . 6 EXERCISES Evaluate each expression. Write all answers without exponents. 1. 822 2. 324 5. 2 1 23 2 22 3 0 4. a2 b 4 6. 2 1 2322 2 1 22 7. a b 6 4 23 8. a b 3 3. 5 0 Simplify each expression. Assume that all variables represent positive real numbers. Write answers with only positive exponents. 9. 11. 13. 15. 422 4 89 . 827 823 7212 .
5 32. 2 2 "6 2 1 "2 1 34. "5 1 "2 5 "y 2 "5 38. "x 2 "x 1 1 40. 6 "r 2 "3 y25 "x 1 "x 1 1 36. "5 "m 2 "5 "z 2 1 "z 2 "5 "p 1 "p2 2 1 "p 2 "p2 2 1 Simplify each root, if possible. 23. "16 2 8x 1 x2 Rationalize each numerator. Assume that all radicands represent positive real numbers. 25. "4 2 25z2 41. 24. "9y2 1 30y 1 25 26. "9k2 1 h2 Rationalize each denominator. Assume that all radicands represent positive real numbers. 27. 29. 5 "7 23 "12 28. 30. 5 "10 4 "8 43. 1 1 "2 2 "x 1 "x 1 1 "x 2 "x 1 1 YOUR TURN ANSWERS 1.
5x 1 2 5 8 2 3x 2 1 3 4. k 2 k 1 5 3 8 2 3. 7 5. 3r 1 2 2 5 1 r 1 1 2 5 6r 1 4 7. 2 3 3m 2 2 1 3 2 m 2 2 4 4 5 6m 2 4 Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places. 9. x2 1 5x 1 6 5 0 10. x2 5 3 1 2x 11. m2 5 14m 2 49 14. m 1 m 2 7 2 5 210 13. 12x2 2 5x 5 2 2 2 23. 2r 2 7r 1 5 5 0 24. 2x2 2 7x 1 30 5 0 25. 3k2 1 k 5 6 26. 5m 2 1 5m 5 0 YOUR TURN ANSWERS 1.