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!

Factoring two variable function

  1. May 7, 2016 #1
    1. The problem statement, all variables and given/known data

    How to factor 2x^2 - (p-2)x - p ??

    2. Relevant equations
    Basic factoring

    3. The attempt at a solution

    I don't know how to do it.
    The answer is 2(x-p/2)(x+2/2)..
    Help me please..
     
  2. jcsd
  3. May 8, 2016 #2

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    By finding its roots?
     
  4. May 8, 2016 #3
    Using quadratic roots formula?
    It seems pretty complicated
     
  5. May 8, 2016 #4

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    Yes.
    It's very easy, you just need to pick that pen of yours and work it out on a paper.
     
  6. May 8, 2016 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    As Blue Leaf posted, that will certainly work, but there is often an easier way. Assuming it has reasonable factors, you can factorise the first and last coefficients. This yields the only possibilities as (x ....)(2x...) and (... 1)(... p). There are two ways of merging those, and some number of options for the sign in between.
    I think there is actually a theorem about this.
     
  7. May 8, 2016 #6
    Aha!

    2x^2 + 2x - px - p= 0
    2x (x+1) - p (x+1) =0
    (2x-p)(x+1)=0

    Thanks a lot! :D
     
  8. May 8, 2016 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

  9. May 8, 2016 #8

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Looks as if it's all solved very nicely.

    Rather than considering this as a two variable function, I would consider p to be a parameter and x to be a variable, the independent variable. So ##\ 2x^2 - (p-2)x - p \ ## is a quadratic (degree 2 polynomial) in ##\ x\ .##

    They way you factored this expression is very sensible.
    Expanding the middle term gives a polynomial with 4 terms. A classic method for factoring a 4 term polynomial is called factoring by grouping, which is what you did.

    In your case you might consider it to be good fortune that, you were given a quadratic in x, which could be expressed as a factorable 4 term polynomial.

    The suggestion of blue_leaf77 in post #2, was also good advice. Whatever the method of finding the two zeros (roots to ##\ ax^2+bx+c=0\ ##), if those two zeros are ##\ s_1\ ## and ##\ s_2 \ ##, then the polynomial factors as follows.
    ##ax^2+bx+c = a(x-s_1)(x-s_2)##​

    .Notice that the roots to you final equation in post #6 are x = p/2, -1 .

    This gives the factoring you gave in post #1.
    ## 2x^2 - (p-2)x - p = 2(x - p/2)(x +1) ##​
     
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: Factoring two variable function
Loading...