1. Not finding help here? Sign up for a free 30min 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!

Factor question

  1. Mar 19, 2013 #1
    1. The problem statement, all variables and given/known data


    given f(x) = x^3 - 6x^2 + 3x + 10

    (a) Factorize f(x)
    (b) if k is a positive integer such that HCF of f(x) and f(x+k) is linear.
    (i) find value of k
    (ii) find LCM of f(x) and f(x+k)





    2. Relevant equations


    I have no problem with (a) and f(x) = (x+1) (x^2 - 7x + 10)

    I have problem with (b) (i) and (ii), I only know that HCF is linear means that there is only one factor which is linear. And that's it. I know nothing further to solve the questipn


    3. The attempt at a solution
     
  2. jcsd
  3. Mar 19, 2013 #2

    eumyang

    User Avatar
    Homework Helper

    Do you need a complete factorization? If so, you are not finished. x2 - 7x + 10 is factorable.
     
  4. Mar 19, 2013 #3
    i have factored f(x) into (x+1)(x-5)(x-2)
    but no idea to go further
     
  5. Mar 19, 2013 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What are the factors of f(x+k)?
     
  6. Mar 19, 2013 #5

    eumyang

    User Avatar
    Homework Helper

    Using the factored form of f(x), find f(x+k).

    I'm assuming that HCF=GCF (greatest common factor). You are looking for a positive k such that there is a linear common factor between f(x) and f(x+k). So one of the three factors of f(x) should also be a factor of f(x+k). I used trial and error to find such a k. Find a k so that when you plug into the factored form of f(x+k), one of its factors is also a factor of f(x).


    (Hope I'm not giving away too much here.)
     
  7. Mar 19, 2013 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Yes, I think you are.
     
  8. Mar 19, 2013 #7
    hi how about LCM?
     
  9. Mar 19, 2013 #8

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Well, what about it? What work have you done on it so far?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Factor question
  1. Factoring question (Replies: 4)

  2. Factoring question (Replies: 8)

  3. Factoring question (Replies: 2)

  4. Factoring question (Replies: 17)

  5. Factoring question (Replies: 4)

Loading...