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

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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It is useful for simplifying algebraic expressions, for solving certain types of equations, and for numerical work. When we write JC2 + 5x + 6 = (x + 2)(x + 3), 10. Factoring we are factoring the left-hand side. If a given polynomial has integer coefficients, we generally look for factors with integer coefficients. A familiar kind of factoring is removing a common polynomial factor. Examples: x4 (3x - _ 6χ3 _ Ίχ2 = χ 2( χ 2 1)(JC2 + 4) + 2(3* - _ 6 χ _ 7)? 1)(4JC + 5) + (Sx - l) 2 = (3JC - l)[(x2 + 4) + 2(4* + 5) + (3* - 1)] = ( 3 J C - l)(x2 + 11JC+ 13).

22. 24. 26. 28. (JC-4)(JC-7) (8JC - 3)(JC + 2) (2JC - 1)(JC2 + 3JC + 2) (2JC3 - 1)(-JC 2 + JC) (JC4 - 3JC)(2JC2 + 5JC + 1) (JC + 1)(JC + 2)(JC + 3) (JC + 1)(JC4 - JC3 + JC2 - JC + 1). 9. Polynomials in Several Variables 35 31. ) Can you see a pattern? 32. (1 - JC)(1 + JC) 34. ) (1 - JC)(1 + JC)(1 4- JC 2 )(1 + JC4) 36. 37. (1 - JC2)(1 4- x 4- x2 4- x3 + x4) (x2 + x + 1)(JC2 - x + 1) 38. (JC2 + 2x + 2)(JC 2 - 33. ) (I - x)(\ 4- JC)(1 4- x2) 35. ) Can you see a pattern? 2JC + 2). Express in the form anxn + · · · 4- a2x2 + axx 4- fl0: 39.

Rules for square roots Let a and b be positive real numbers. Then (2) Va^ = a, (1) {Va? = a, (3) Väb - Vä Vb, Vb Vb Rules (1) and (2) come directly from the definition of square roots. To check rule (3), let Vä = r and y/b = s. Then a = r2 and b = s2, hence ab = r2s2 = (rs)2. This says that ^fäb = rs = \fa Λ/Ϊ>. Rule (4) is checked similarly. Warning: These rules concern only multiplication and division. Square roots have no simple behavior with respect to addition and subtraction. In particular, VâT~b IS NOT Va+ Vbl For example, \/25 = \/9 + 16 and V25 = 5, but 5 φ y/9 + VÏ6 = 3 + 4 = 7.

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