anonymous one year ago Organize the following polynomial expressions from least to greatest based on their degree: x + 2xyz 9x3y2 18x2 + 5ab − 6y 4x4 + 3x2 − x − 4

1. anonymous

$x + 2xyz=x + 2x^1y^1z^1$ has degree $$1+1+1=3$$

2. anonymous

$9x^3y^2$ has degree $$3+2=5$$

3. anonymous

i bet you can do the rest

4. anonymous

if not, i can check

5. anonymous

would this be number three? $18^2 +5a^1b^1-6y^-1$

6. anonymous

that's -6y^1 but I think the one is negative

7. anonymous

$18x^2 + 5ab − 6y$ has degree 2

8. anonymous

oh okay so if it doesn't show an exponent then you kind of make your own

9. anonymous

yeah i have a feeling you don't quite get this am i right?

10. anonymous

yup

11. anonymous

ok here is a polynomial with three terms $xy^2+x^2y^2+2xy$

12. anonymous

each term has a degree ' the degree of $xy^2$ is $1+2=3$ th degree of $$x^2y^2$$ is $$2+2=4$$ and the degree of $$2xy$$ is $$1+1=2$$

13. anonymous

so the degrees are the exponents added up

14. anonymous

the "degree of the polynomial" is the degree of the term of highest degree, so the degree of $xy^2+x^2y^2+2xy$ is $$4$$

15. anonymous

yes, the degree of each term is the sum of the degrees of each variable so for example the degree of $$xy^2z^4$$ is $$7$$

16. anonymous

and whichever has the highest degree is the degree of the polynomial?

17. anonymous

sorry if I repeat things, just trying to get it through to myself

18. anonymous

that is fine

19. anonymous

you are right, the degree of the polynomial is the degree of the term of highest degree

20. anonymous

so for example if you just have on variable, the degree of say $2x^5+3x^2+5x+1$ is $$5$$ but if you have more than one variable you have to add the degrees of each variable

21. anonymous

with that in mind, what is the degree of $4x^4 + 3x^2 − x − 4$?

22. anonymous

the degree of the polynomial would be 4 because of 4x^4

23. anonymous

yes

24. anonymous

$4x^4+3x^2-x-4$ first set has a degree of four, second set has a degree of two, and the third I think it's one but I'm not sure if it's negative one

25. anonymous

a polynomial cannot have a term of negative degree

26. anonymous

x + 2xyz degree of 3 9x3y2 degree of 5 18x2 + 5ab − 6y degree of 2 I'm pretty sure 4x4 + 3x2 − x − 4 4

27. anonymous

yes

28. anonymous

okay gotcha

29. anonymous

btw the degree of a constant is zero

30. anonymous

III, I, IV, II IV, I, II, III III, II, IV, I IV, III, I, II these were the answer choices btw lol

31. anonymous

what's a constant?

32. anonymous

lol i will let you order them yourself, you got them all right

33. anonymous

it's a

34. anonymous

$x^2-5x+\color{red}3$ the constant is $$\color{red}3$$

35. anonymous

yeah it is A

36. anonymous

so one with no exponent or variable, just a flat out number

37. anonymous

right called a "constant" because it does not depend of what $$x$$ is

38. anonymous

i have a question do you know what \$2x^3+5x^2+4x+7$ is if $$x=10$$?

39. anonymous

$2(10)^3+5(10)^2+4(10)+7$ $2(1,000)+5(100)+40+7$ two thousand five hundred and forty seven

40. anonymous

right so you see we write our whole numbers as polynomials, using base ten (instead of x)

41. anonymous

$2(10)^3+5(10)^2+4(10)+7=2547$

42. anonymous

keep that in mind when you learn to add, subtract and multiply polynomials it works pretty much the same way as with whole numbers of course there are some differences, but it is basically the same

43. anonymous

okay :-) can you help me with some more questions?

44. anonymous

it's like two or three more, one I think I got down

45. anonymous

sure

46. anonymous

4x^2 + 3xy + 12yz this would be a second degree trinomial correct?

47. anonymous

yes

48. anonymous

okay that's what I put, next one

49. anonymous

Organize the following expressions from greatest to least by number of terms: x + 2xyz 9x2yz 18x2 + 5ab − 6y 4x3 + 3x2 − x − 4 Answers: III, IV, I, II IV, I, II, III IV, III, I, II III, II, IV, I

50. anonymous

Is it C?

51. anonymous

Because I think that terms are the sets in the polynomial

52. anonymous

the "number of terms"? yeah we can count for sure

53. anonymous

you are right, it is C

54. anonymous

Which statement best demonstrates why the following is a non-example of a polynomial? $\frac{ 33y^2 }{ x^2 } - 62y^2xz-35z^2y^2$ The expression has a variable raised to a negative exponent. The expression has a negative coefficient. The expression has a variable raised to a fraction. The expression has a variable in the denominator of a fraction.

55. anonymous

I feel like it's C again

56. anonymous

not this time

57. anonymous

a polynomial cannot have a variable in the denominator

58. anonymous

" The expression has a variable raised to a fraction." actually makes no sense at all go with D

59. anonymous

oh okay, I thought fractions weren't supposed to be in polynomials period lol

60. anonymous

unless it means something iike $x^{\frac{2}{3}}$which is NOT a polynomial

61. anonymous

the coeficients can be fractions $\frac{4}{5}x^2$ is a polynomial

62. anonymous

Last one :) Which of the following shows 9x^2y − 4x + 3y^3x − 2y^2 written in standard form? 9x^2y − 4x + 3y^3x − 2y^2 3y^3x − 2y^2 + 9x^2y − 4x 9x^2y − 4x − 2y^2 + 3y^3x 3y^3x + 9x^2y − 2y^2 − 4x

63. anonymous

standard form means order the terms from highest degree to lowest degree

64. anonymous

Then D

65. anonymous

yes

66. anonymous

I got a one hundred, thank you so much!!

67. anonymous

yay yw see you in lala land

68. anonymous

Lol! I'll probably need help tomorrow, will you still be on?

69. anonymous

always glad to help someone who is actually trying

70. anonymous

probably you can always tag me if you like

71. anonymous

Okay :) thank you so much, I have to go to sleep now. Good night!

72. anonymous

sometime around 9:30 or 10 usually gnight