1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Algebra Question

  1. Dec 7, 2016 #1
    Hi guys, there's a sample problem in m textbook where they simplify an expression from x3-6x2+12x-8/x2-4x+4 to (x-2)3/(x-2)2. Can you explain how they solved this? For reference, I'm learning about limits
     
    Last edited: Dec 7, 2016
  2. jcsd
  3. Dec 7, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I moved the thread to our homework section as the problem is homework-like.

    I guess you mean (x3-6x2+12x-8)/(x2-4x+4). For the denominator, you should be able to find roots, once you know where the denominator gets zero you can also write it as product (here: (x-2)(x-2)). For the numerator, guess a root, then take it out as factor and compute the other factor, then do the same as for the denominator.
     
  4. Dec 7, 2016 #3

    hilbert2

    User Avatar
    Science Advisor
    Gold Member

    Knowledge of the fact that one root of a cubic polynomial with integer coefficients is a divisor of the constant term (here 8) will help in guessing.
     
  5. Dec 7, 2016 #4
    Uh, yeah, I missed the big notice at the top... Had a couple glasses of wine :oops::H

    Ok, so I guessed root 2 (lol). Would I then just divide out factor (x-2), like polynomial long division, or is there an easier way I'm overlooking?
     
  6. Dec 7, 2016 #5

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Polynomial long division is the right approach - unless you directly see or guess that the numerator is (x-2)3 (possible with practice), then you can skip those steps.
     
  7. Dec 7, 2016 #6
    Ok thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted