Question
upstudy study bank question image url

Factor completely. \( 5 w-10 w^{2}+2 w^{4}-w^{3} \)

Ask by Martin Gordon. in the United States
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The expression factors to \(w(1-2w)(5-w^{2})\).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Extra Insights

To factor the expression \( 5w - 10w^2 + 2w^4 - w^3 \), we can first rearrange the terms in descending order of powers: \( 2w^4 - w^3 - 10w^2 + 5w \). Now, we can factor by grouping. Let's group the first two terms and the last two terms: \( (2w^4 - w^3) + (-10w^2 + 5w) \). From the first group, we can factor out \( w^3 \): \( w^3(2w - 1) \). From the second group, we can factor out \(-5w\): \( -5w(2w - 1) \). Now, we have: \( w^3(2w - 1) - 5w(2w - 1) \). We can factor out the common factor \( (2w - 1) \): \( (2w - 1)(w^3 - 5w) \). Next, the second factor \( w^3 - 5w \) can be factored further by taking out \( w \): \( w(w^2 - 5) \). Putting it all together, we have: \( (2w - 1)w(w^2 - 5) \). So the completely factored form of \( 5w - 10w^2 + 2w^4 - w^3 \) is: \[ (2w - 1)w(w^2 - 5). \]

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy