By Harley Flanders and Justin J. Price (Auth.)

Algebra and Trigonometry

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**Extra resources for Algebra and Trigonometry**

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JC 4- a)(x ^ b) - (x -h a)(x 4- c) 43. (x2 4- 1)(2JC - 1) + (x2 + 1)(JC2 + 2) 44. JC(3JC2 + JC - 46. ( x 2 + C)(JC2 - 1) + (x 4- 1)(JC2 4- 2JC) 45. (ax + £)(&* + à) d). Find the coefficient of JC3 in the product: 47. (JC2 4- 3JC + 1)(2JC - 48. (JC3 - 1) 7JC H- 6)(JC 2 4- 1) 49. JC2(2JC - 50. (JC + 1)(2JC - 5)(JC 4- 6) 51. (JC4 - 52. (JC3 4- 2JC2 4- 3JC 4- 4)(6JC 3 4- lx2 53. (1 + JC 3 )(1 4- JC4)(1 4- JC 5 )(1 4- Je6) 1)(4JC - 1) 6JC3 + 2JC2 4- 5JC 4- 2)(JC 3 + JC + 4) - JC - 54. (1 4- 2JC)(1 4- 3 x 2 ) ( l 4- 4JC 3 )(1 + 5JC 4 ) 55.

We call r the «-th root of a and write r = ^/ä. The symbol >/~ is again called a radical. ) As with the square root, we shall write S/O = 0 because 0 n = 0. Examples: \/64 = 4 because 4 3 = 64, V^T = 3 because 3 4 = 81. Remark 1: If « is even, then ( —r)n = rw, so — v ^ is also an n-th root of a, a number whose w-th power is a. However, as with square roots, the symbol ~\/ä always means the unique positive n-th. root of a for a > 0. Remark 2: If n is odd, then negative numbers also have n-th roots.

Express in terms of at most a single radical: 25. y/2-yï 26. VT^ 29. ( - A ) * 30. VbVb 27. {tf/γϊό 28. -^2L 31. V^-V^-V^ 3 32. V^-V^'V^· Express without radicals, using only positive exponents: 33. d/xj2)-3'5 34. -s/{xy2)-w3/(x2y)-wt 35. (\/jc 14 y- 21/5 )- 3 / 7 36. 4/5 JÖ · \ y ) \ z ) \ w ) \ χ ) ' 8. POLYNOMIALS In this section we study properties of the most common algebraic expressions, polynomials. A polynomial is an algebraic expression of the type a0 + axx + a2x2 + . . + anxn, 32 1. BASIC ALGEBRA where a0, a1, a2, · · ·, an are real numbers called the coefficients of the polynomial.