homework

Sarah Owens 1. When the numerator and denominator of a rational expresseioncontain no common factors (except 1 and -1), the rational expression is in Lowest Terms. 4. False. The LCM would be 6x^3(x+1). Reduce to Lowest terms 7. x^2-2x = x(x-2) = x _____________________ 3x-6 = 3(x-2) = 3 10. x^2+4x=4 = (x-4)(x+16) = (x+2) __________ _____________ ________ x^2 - 16 (x+16)^2 (x+4) 13. x^2+4x-5 = (x+5)(x-1) =(x+5) __________________________________ x^2-2x+1 (x-1)^2 (x-1) 16. 2x^2+5x-3 ?? ___________ 1-2x Perform indicated operation and simplify the result. 19. 4x^2 times x-4 4x^2 times x-4 2x _____ _____ = ______ _____ = ____ x^2-16 2x (x-4)(x+4) 2x x+4 22. ?? 25. 6x = 6x times 2x+4 = 6x times 2(x+2) = 4x _________ _______ _________ ___________ __________ ________ x^2 - 4 x^2 - 4 3x-9 (x-2)(x+2) 3(x-3) (x-2)(x-3) _____________ 3x - 9 ________ 2x + 4 28. ?? 31. x^2 + 7x + 12 = x^2 + 7x + 12 times x^2 - x - 12 = _______________ _______________ ______________ x^2 + 7x + 12 x^2 + 7x + 12 x^2 + x - 12 _______________________________________________________________ x^2 + x - 12 = (x+3)(x+4) times (x-4)(x+3) = = (x+3)^2 _______________ _____________ ______________ _________ x^2 - x - 12 = (x-3)(x-4) (x+4)(x-3) (x-3)^2 34. 9x^2 + 3x - 2 = (3x + 2) (3x - 1) __________________ ___________________ = (3x + 2)(3x - 1) times (4x+1)(2x-3) = (4x+1)(2x-3)

12x^2 + 5x - 2 (4x - 1) (3x +2) __________________ ______________ _____________ _______________________________________________ (4x-1)(3x+2) (3x-1)(2x-3) (4x-1)(3x-1)

9x^2 - 6x +1 (3x - 1) (3x - 1) _____________ ___________________ 8x^2 - 10x - 3 (4x + 1) (2x - 3) Perform operations and simplify. 37. x^2 - 4 = x^2 - 4 = (x+2)(x-2) _______ _______ __________ ______________ 2x - 3 2x - 3 2x - 3 2x - 3

40. 2x - 5 + x+4 = 2x - 5 = 4x _________ __________ _________ ________ 3x + 2 3x + 2 3x + 2 3x + 2

This is not correct. 2x - 5 isn't equal to 4x, and 2x - 5 + (x + 4) is 3x + 1.

43. 4 + x = 4 + x = 4-x ______ _______ ____________ _________ x-2 2-x x-2 x-2 46. ?? 49. x-3 - x+4 = (x+4)(x+2) = -11x - 2 = 11x + 2 = x^2 - 5x + 6 - (x^2 + 6x + 8) ______ _______ ______________ _____________ _____________ ________________________________ x+2 x-2 (x-2)(x+2) (x+2)(x-2) (x+2)(x-2) (x+2)(x-2) 52. x-1 + x = x-1 ______ _____ _______ x^3 x^2+1 x^5 + 1

The denominator is x^3 ( x^2 + 1) = x^5 + x^3; the numerator of the correct answer is x^4 + 2 x^3 - x^2 + x - 1. I don't immediately see any common factors.

Find the LCM of each polynomial. 55. x^3-x, x^2 - x = x^2 - x = x(x-1) = x(x^2 - 1) = x(x+1)(x-1) LCM = x(x+1)(x-1) 58. x-3, x^2 + 3x, x^3 - 9x = x(x-3) (x+9) is the LCM Perform and simplify 61. x - x = x - x = x(x+4) - x(x-1) = _______________ __________________ ________________ ______________ ______________ ______________ x^2 - 7x + 6 x^2 - 2x - 24 (x-6)(x-1) (x-6)(x+4 (x-6)(x-1)(x+4) (x-6)(x+4)(x-1) x^2 + 4x - x^2 + x = 5x _______________________ ____________________________ (x-6)(x+1)(x-1) (x-6)(x+4)(x-1)

I can't read this problem.

64. ?? 67. ?? 70. ?? "

I've made a couple of notes. It's difficult to read your work in this format--you should be using the 'typewriter notation' format introduced in the orientation.

Overall you seem to be doing pretty well here, but there are some errors. I've indicated a couple of them.

You should be submitting these assignments using the query program, as indicated in the orientation.

Let me know if you have questions.