Results 1 to 5 of 5

Thread: Factoring With Respect to the Integers

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    8

    Factoring With Respect to the Integers

    I'm a little bit stuck on a few of my homework problems, and can't really find out how to do them in my text book. I don't really need help on both of them unless there're different ways to find the answer, I just need to learn how to solve them. Any help would be fantastic.
    Thanks in advance,
    Mackenzie

    "Completely factor the polynomial with respect to the integers"
    1. x2-9x-22
    2. 2x2-5x+2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    Wahiawa, Hawaii
    Posts
    679
    Thanks
    1
    Quote Originally Posted by mackenzie25 View Post
    I'm a little bit stuck on a few of my homework problems, and can't really find out how to do them in my text book. I don't really need help on both of them unless there're different ways to find the answer, I just need to learn how to solve them. Any help would be fantastic.
    Thanks in advance,
    Mackenzie

    "Completely factor the polynomial with respect to the integers"
    1. x2-9x-22
    2. 2x2-5x+2
    given your expressions do you mean

    1. $\displaystyle x^2-9x-22$
    2. $\displaystyle 2x^2-5x+2$

    if so

    1. $\displaystyle (x-11)(x+2)$
    2. $\displaystyle (2x-1)(x-1)$ or $\displaystyle 2(x-2)(x-.5)$

    there is no roots since these are not equations just expressions
    Last edited by bigwave; Dec 28th 2009 at 01:24 PM. Reason: more info
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    8
    That's definitely what I was going for, but how did you factor it?
    (Thanks! )
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    Wahiawa, Hawaii
    Posts
    679
    Thanks
    1
    $\displaystyle ax^2 + bx + c$ where $\displaystyle a, b, c $, are real numbers

    $\displaystyle
    (mx+p)(nx+q)
    $
    where

    $\displaystyle
    mn = a, pq = c
    $
    and

    $\displaystyle
    pn + mq = b
    $
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    4
    $\displaystyle (5)(7)=(3+2)(3+4)=3(3+4)+2(3+4)=3^2+3(4)+2(3)+2(4)$

    $\displaystyle =3^2+[3(4)+2(3)]+2(4)=35$

    $\displaystyle Such\ an\ alternative\ allows\ us\ to\ expand\ (x+a)(x+b)$
    $\displaystyle to\ x(x+b)+a(x+b)=x^2+(a+b)x+ab$

    $\displaystyle Also\ (5)(7)=(9-4)(9-2)=9^2+9(-4-2)+(-4)(-2)=35$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: Aug 3rd 2010, 01:31 PM
  2. Matrix of integers whose inverse is full of integers
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Mar 19th 2010, 02:02 PM
  3. G(x) in respect to F(X)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Mar 18th 2009, 07:23 PM
  4. Replies: 4
    Last Post: Feb 24th 2008, 03:08 PM
  5. respect to x
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Nov 2nd 2007, 02:01 PM

Search Tags


/mathhelpforum @mathhelpforum