Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

yociyoci Group Title

How to factor: x^5-6x^4+40x^2-13x-70 Please show me the steps!

  • one year ago
  • one year ago

  • This Question is Closed
  1. ArkGoLucky Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    There is a theorem thing that states that plus or minus the factors of the constant(70 in this case) divided by plus or minus the constant in front of the term with the largest power are all the possibilities of the factors of the polynomial. So just start crunching the numbers.

    • one year ago
  2. ArkGoLucky Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    try \[\pm1,2,5,7,10,35,70\]then use synthetic division or polynomial long division to divide out the factors

    • one year ago
  3. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    can you explain synthetic divsion please?

    • one year ago
  4. ArkGoLucky Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    let finish solving the problem and then I will explain

    • one year ago
  5. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Then, can you please show the steps for doing the polynomial long division to divide out the factors

    • one year ago
  6. ArkGoLucky Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    there is only one integer factor: (x-2). |dw:1357004129003:dw|

    • one year ago
  7. ArkGoLucky Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the other factor is (x-2)

    • one year ago
  8. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    What are the numbers of the thrid and forth row?

    • one year ago
  9. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh, I am beginning to see how synethetic divsion works

    • one year ago
  10. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Please correct me if I am going to wrong way: x^5-6x^4+40x^2-13x-70 =(x-2)(x^4-4x^3-8x^2+24x+35) The next step would be to divide (x^4-4x^3-8x^2+24x+35) by 5 using synethetic divsion?

    • one year ago
  11. LogicalApple Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    The remaining factors are not rational, so the rational roots theorem would not assist us any further.

    • one year ago
  12. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh, no wonder it didn't work anymore

    • one year ago
  13. ArkGoLucky Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so that's how you factor it

    • one year ago
  14. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    (x-2)(x^4-4x^3-8x^2+24x+35) This is the simplest form? Can't (x^4-4x^3-8x^2+24x+35) be factor too?

    • one year ago
  15. LogicalApple Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Since the remaining roots are complex, you couldn't factor out a single term, you would have to somehow factor out a quadratic. I do not know any techniques that will do this.

    • one year ago
  16. LogicalApple Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Not complex, irrational. But they exist as conjugates so you would have to factor out a quadratic instead of a single term.

    • one year ago
  17. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, i will continue to try

    • one year ago
  18. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I got it (x^4-4x^3-8x^2+24x+35)=(x^2-2x-7)(x^2-2x-5)

    • one year ago
  19. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so when (x^5-6x^4+40x^2-13x-70) is factored, it will be (x-2)(x^2-2x-7)(x^2-2x-5) Is it correct?

    • one year ago
  20. LogicalApple Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes. That's it !

    • one year ago
  21. mathmate Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @yociyoci just curious, how did you factorize it?

    • one year ago
  22. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you so much everyone for helping me with factoring! I learnt so much from you guys!! Thanks!!

    • one year ago
  23. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I plug in variables and did some algebra and trial and error

    • one year ago
  24. LogicalApple Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    o_o

    • one year ago
  25. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ya, it was long...

    • one year ago
  26. mathmate Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You can also use some facts as we usually do in quadratics. Assume (x^2+ax+b)(x^2+cx+d) then (a+c)=-4 ac+b+d=-8 bc+ad=24 bd=35 Hopefully this will help you eliminate cases quickly without having to multiply out the whole expression.

    • one year ago
  27. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ya, I did something similar

    • one year ago
  28. LogicalApple Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    That's a really good technique.

    • one year ago
  29. mathmate Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Great! Thank you for the enjoyable session!

    • one year ago
  30. yociyoci Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you very much, guys!! :)

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.