Results 1 to 3 of 3
Like Tree2Thanks
  • 1 Post By romsek
  • 1 Post By greg1313

Thread: High school maths question

  1. #1
    Newbie
    Joined
    Aug 2019
    From
    Australia
    Posts
    1

    High school maths question

    I need to understand how to get from:

    42x^2 - 9x - 6

    to

    3(2x-1)(7x+2)

    sorry if it's in the wrong spot!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    6,580
    Thanks
    2913

    Re: High school maths question

    the systematic way would be

    $42x^2 - 9x-6 = 42\left (x^2 - \dfrac{3}{14} - \dfrac 1 7\right)$

    Now use the quadratic equation to find the roots of the quadratic in parens

    $x = \dfrac{\dfrac{3}{14} \pm \sqrt{\dfrac{9}{196}+\dfrac 4 7}}{2} = \dfrac{\dfrac{3}{14}\pm \dfrac{11}{14}}{2} = \dfrac 1 2,~-\dfrac 2 7$

    So then we have our original polynomial is given by

    $42\left(x-\dfrac 1 2\right)\left(x + \dfrac 2 7\right) = 3(2x-1)(7x+2)$
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Dec 2016
    From
    Earth
    Posts
    282
    Thanks
    148

    Re: High school maths question

    Quote Originally Posted by Molly123456 View Post

    42x^2 - 9x - 6

    3(2x-1)(7x+2)
    $\displaystyle 3(14x^2 - 3x - 2) $

    a*c method

    14*(-2) = -28

    You want two integer divisors of -28 which when
    multiplied together give -28 and which add to -3.

    -7 and 4 work.

    Use them as coefficients on the first degree x-terms,
    rewrite the polynomial, and then factor by grouping
    on either of the next two versions that follow:

    $\displaystyle 3[14x^2 + 4x - 7x - 2] \ \ \ or $

    $\displaystyle 3[14x^2 - 7x + 4x - 2] \ =$

    $\displaystyle 3[7x(2x - 1) \ \ \ ?(2x - 1)] \ =$

    $\displaystyle 3[7x(2x - 1) \ + \ 2(2x - 1)] \ = $

    $\displaystyle 3(2x - 1)(7x + 2)$
    Last edited by greg1313; Aug 11th 2019 at 05:27 AM.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: Aug 22nd 2014, 04:08 AM
  2. High School Maths problem Sum
    Posted in the Math Challenge Problems Forum
    Replies: 2
    Last Post: Jul 13th 2012, 07:48 AM
  3. high school algebra question
    Posted in the Algebra Forum
    Replies: 8
    Last Post: Mar 10th 2010, 06:59 AM
  4. Replies: 1
    Last Post: Nov 30th 2008, 11:00 AM
  5. Grade 11 High School Circles Question
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Nov 30th 2008, 09:35 AM

/mathhelpforum @mathhelpforum