Question
upstudy study bank question image url

Factor. \( 27 p^{2}-90 p+63 \) \( \square \) Submit

Ask by Fuentes Cummings. in the United States
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The factored form is \(9(p-1)(3p-7)\).

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

The Deep Dive

To factor \( 27 p^{2}-90 p+63 \), we start by looking for the greatest common factor (GCF) of the coefficients. The GCF is 9. So, we can pull it out first: \( 9(3p^{2}-10p+7) \) Next, we need to factor the quadratic expression \( 3p^{2}-10p+7 \). We look for two numbers that multiply to \( 3 \cdot 7 = 21 \) and add to \(-10\). These numbers are \(-3\) and \(-7\): Rewrite the quadratic as: \( 9(3p^{2}-3p-7p+7) \) Now, group the terms: \( 9((3p^{2}-3p)-(7p-7)) \) Factoring gives us: \( 9(3p(p-1)-7(p-1)) \) This leads to: \( 9(p-1)(3p-7) \) So the final factored form is: \( 9(p-1)(3p-7) \)

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