Facebook Page
Twitter
RSS
+ Reply to Thread
Results 1 to 4 of 4
  1. MHB Craftsman

    Status
    Online
    Join Date
    Jul 2016
    Posts
    336
    Thanks
    444 times
    Thanked
    159 times
    Trophies
    2 Highscores
    Awards
    MHB Model User Award (2016)
    #1
    I was wondering whether this expression could be factored by any means

    $x^2+4x-1$


    Many THanks

  2. Philosophus Nātūrālis
    MHB Math Scholar
    MHB POTW Director
    MHB Ambassador

    Status
    Offline
    Join Date
    Jan 2012
    Location
    Raleigh, NC
    Posts
    3,551
    Thanks
    9,481 times
    Thanked
    8,574 times
    Thank/Post
    2.415
    Trophies
    1 Highscore
    Awards
    MHB Math Notes Award (2016)  

MHB Math Notes Award (2015)
    #2
    Not over the rationals, but if you multiply out $\left(x+\sqrt{5}+2\right)\left(x-\sqrt{5}+2\right)$, I fancy you'll get your original expression back. Wolfram|Alpha is a great way to check these sorts of things. You can use the quadratic formula to get it by hand (set your quadratic equal to zero).

  3. MHB Craftsman
    MHB Math Helper

    Status
    Offline
    Join Date
    Jan 2012
    Posts
    488
    Thanks
    205 times
    Thanked
    575 times
    Thank/Post
    1.178
    #3
    Or you could use the quadratic formula to show that $ \displaystyle x^2+ 4x- 1= 0$ has roots $ \displaystyle \frac{-4\pm\sqrt{4^2- 4(1)(-1)}}{2(1)}= \frac{-4\pm\sqrt{16+ 4}}{2}= \frac{-4\pm\sqrt{20}}{2}= \frac{4\pm2\sqrt{5}}{2}= 2\pm\sqrt{5}$ so that its factors are $ \displaystyle (x- 2- \sqrt{5})(x- 2+ \sqrt{5})$.

    Or "complete the square": $ \displaystyle x^2+ 4x- 1= x^2+ 4x+ 4- 4- 1= (x- 2)^2- 5= (x- 2)^2- (\sqrt{5})^2$, a "difference of two squares" which can be factored as a "sum and difference", $ \displaystyle (x- 2+ \sqrt{5})(x- 2- \sqrt{5})$.
    ($ \displaystyle a^2- b^2= (a+ b)(a- b)$)

  4. MHB Apprentice

    Status
    Offline
    Join Date
    Sep 2014
    Posts
    56
    Thanks
    13 times
    Thanked
    26 times
    #4
    Complete The Square Method:
    $x^2 + 4x - 1 $
    $= x^2 + 4x + 4 - 4 - 1$
    $ = (x + 2)^2 - 5$
    $ = (x + 2)^2 - (\sqrt{5})^2$
    $ = (x + 2 + \sqrt{5})(x + 2 - \sqrt{5})$

Similar Threads

  1. Simpify Factored Form Equation
    By kato in forum Pre-Algebra and Algebra
    Replies: 3
    Last Post: September 26th, 2016, 07:56
  2. Replies: 2
    Last Post: July 2nd, 2016, 20:40
  3. Expression value
    By jacks in forum Pre-Algebra and Algebra
    Replies: 0
    Last Post: April 19th, 2016, 14:02
  4. Replies: 2
    Last Post: November 24th, 2015, 20:23
  5. d in the expression
    By topsquark in forum Linear and Abstract Algebra
    Replies: 3
    Last Post: October 7th, 2014, 17:53

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
Math Help Boards