Results 1 to 5 of 5

Math Help - factoring trinomial squares

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    2

    factoring trinomial squares

    Hi, Im having difficulty factoring completely. Ive been running into this problem over again.

    heres an example:

    5y4 + 10y2 + 5

    I ended up with:

    5y(y3 + 1) 5(Y + 1)

    the correct answer is:

    5(y2 + 1)2

    how do I know what Im supposed to completely factor? is there a rule Im fogetting? initially, I thought I was suppose to factor out all exponents but I found that not to be true.

    heres another:

    12p3 + 31p2 + 20p
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by mathtoe View Post
    Hi, Im having difficulty factoring completely. Ive been running into this problem over again.

    heres an example:

    5y4 + 10y2 + 5

    I ended up with:

    5y(y3 + 1) 5(Y + 1)

    the correct answer is:

    5(y2 + 1)2

    how do I know what Im supposed to completely factor? is there a rule Im fogetting? initially, I thought I was suppose to factor out all exponents but I found that not to be true.

    heres another:

    12p3 + 31p2 + 20p
    5y^4 + 10y^2 + 5

    Let y^2 = u

    =5u^2 + 10u + 5

    =(5u + 5)(u + 1)

    Factor out a 5 from the first bracket.

    =5(u + 1)(u + 1)

    =5(u + 1)^2

    But u = y^2

    Thus: =5(y^2 + 1)^2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by mathtoe View Post
    heres another:

    12p3 + 31p2 + 20p
    12p^3 + 31p^2 + 20p

    Factor out a p.

    = p(12p^2 + 31p + 20)

    = p(3p + 4)(4p + 5)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2008
    Posts
    2


    how did you arrive at this?

    I was told to multiply the 1st & last terms and their sum equals the 2nd term. is that what you did? how else can you arrive with the 2 inner terms?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by mathtoe View Post


    how did you arrive at this?

    I was told to multiply the 1st & last terms and their sum equals the 2nd term. is that what you did? how else can you arrive with the 2 inner terms?
    (12p^2 + 31p + 20) = (3p + 4)(4p + 5)

    Basically you have to play around with the factors of 12 and 20.

    For 12, you could have 12&1 ; 6&2 ; 3&4
    For 20, you could have 20&1 ; 10&2 ; 4&5

    Then you have to see which of those coefficients are capable of making 31 for the middle term.

    So write:

    ( \ \ p + \ \ )( \ \ p + \ \ ) (We know both have to be + since the middle and last terms are positive.)

    Now take those possible co-efficients, plug them in, and multiply out. If one set doesnt work, try the next.

    Note that you can also swap the co-efficients around.
    Instead of pairs 3&4 and 4&5 ; you could have 4&3 and 4&5.
    Later on you will have the knack of instinctively knowing which it would probably be.

    I can give you a hint, which is: The co-efficients will often be those close to each other. If we go back to the example of 12, it will most likely be 3&4 (or 4&3) that will work. But this is not always true.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Factoring trinomial
    Posted in the Algebra Forum
    Replies: 8
    Last Post: September 21st 2011, 02:04 PM
  2. Factoring a Trinomial
    Posted in the Algebra Forum
    Replies: 5
    Last Post: March 8th 2010, 01:44 PM
  3. Trinomial factoring help
    Posted in the Algebra Forum
    Replies: 5
    Last Post: August 4th 2008, 04:17 PM
  4. trinomial factoring
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 3rd 2008, 09:48 AM
  5. Need Help Factoring this Trinomial
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 1st 2007, 04:05 PM

Search Tags


/mathhelpforum @mathhelpforum