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Harley Flanders and Justin J. Price (Auth.)'s Algebra and Trigonometry PDF

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

ISBN-10: 012259665X

ISBN-13: 9780122596650

Algebra and Trigonometry

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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. X:2, —JW + ^ x - 2x 3 , 1 + 7x 2 + 8χ 3 - x 5. The degree of a polynomial is the highest exponent occurring with non-zero coefficient.

Rule (3) VA:2 4- 1 46. rule (4). 7, y/5 ^ 2 . 2 to estimate 47. V6 48. VÏÔ 49. VV5 50. 51. V3Ö 52. V75 53. V4Ö 54. Prove: 55. V5 + 2V6 = \/2 + V3 57. V9 - 2 \ / Ï 4 = V7 - \/2 V*2 + 1 V2/3 y/ÏÏ6. 56. yfr - 2 \/6 = \/3 - y/l 58. \/δ + 2 >/Ϊ5 = λ/3 + V5. 7. RATIONAL EXPONENTS What meaning can we give to am/n, where m/n is a rational number not necessarily an integer? If we can define such fractional powers, and if the rules of exponents are to hold, then we should have iam/n\n _ ^(m/n)n = flm This means that am/n must be the «-th root of am.

Poor use of parentheses: WRONG 3(JC 3. + 1) = 3x + 1 RIGHT 3(x + 1) = 3x + 3 (i*)(i>0 = \*y (J*)(iy) = i*y x - (2y + 1) = x - 2y + 1 JC - (2>; + 1) = x - 2y Mistakes with exponents and radicals: WRONG (2JC)3 = 2x3 (x3)4 = x7 RIGHT (2x)3 = 8;c3 (JC3)4 = x12 x3x4 = x12 JC 3JC 4 = JC 7 y/3x~= 3 Vic V3Jc = \/3\/JC. 12. Common Errors in Algebra 47 4. Incorrect use offormulas: RIGHT WRONG 1 x _L + l = £±z 1-_L_ y ~ x +y V* + y = Vx + Vy (x+y)2 = x2+y2 Leave as V* + y(x+y)2 = x2 + 2xy+y2. 5. Sloppy writing: Vx+ i Is it 1 Is it JC-5 Is it Λ:-5 1 2* Is it i* « i' x+y+3 V* + 1 or V* + 1 ?

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Algebra and Trigonometry by Harley Flanders and Justin J. Price (Auth.)


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