Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

zugzwang

  • one year ago

Let's have a little fun: Factor out x⁵ + 2x⁴ + 4x³ + 8x² + 16x + 32

  • This Question is Closed
  1. shubhamsrg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    x^4 (x+2) + 4x^2(x+2) + 16(x+2)

  2. klimenkov
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(S=x^5+2x^4+4x^3+8x^2+16x+32=32\cdot\left(\frac{x^5}{32}+\frac{x^4}{16}+\frac{x^3}{8}+\frac{x^2}{4}+\frac{x}{2}+1\right)\). \(S\cdot\frac x 2=32\cdot\left(\frac{x^6}{64}+\frac{x^5}{32}+\frac{x^4}{16}+\frac{x^3}{8}+\frac{x^2}{4}+\frac{x}{2}\right)\). Subtract the first equation from the second: \(S\cdot(\frac x 2-1)=32\cdot\left(\frac{x^6}{64}-1\right)\). \(S=\frac{\left(\frac{x^3}{8}-1\right)\left(\frac{x^3}{8}+1\right)}{(\frac x 2-1)}=\frac1{(\frac x2-1)}\cdot(\frac x 2-1)(\frac{x^2}4+\frac x 2+1)(\frac x 2+1)(\frac{x^2}4-\frac x 2+1)=\) \(=(\frac{x^2}4+\frac x 2+1)(\frac x 2+1)(\frac{x^2}4-\frac x 2+1)\).

  3. klimenkov
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh.. I forgot 32. \(S=(x^2+2 x+4)( x+2)(x^2-2 x+4)\).

  4. sirm3d
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[x^5+2x^4+4x^3+8x^2+16x+32=\frac{x^6-32}{x-2}\\=\frac{(x^3-8)(x^3+8)}{x-2}=\frac{(x-2)(x^2+2x+4)(x+2)(x^2-2x+4)}{x-2}\\=(x+2)(x^2+2x+4)(x^2-2x+4)\]

  5. sirm3d
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oopd, that should be \[\frac{x^6-64}{x-2}\]

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

    Nice one, @sirm3d, the answer (and process) I was hoping for :)

  7. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.