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!

Solving for x in a trinomial that has a GCF

  1. Jul 17, 2007 #1
    What I am trying to do here is to factor so i can come up with the solutions for x (which are 4 and -3).
    4x[tex]^{2}[/tex] + 4x - 48 = 0

    Here's what I've done to solve so far:
    4(x[tex]^{2}[/tex] - 1x - 12) = 0
    4(x-4)(x+3)=0

    Now I'm not even sure if what I'm doing is right here, but if it is my problem is comming to the solution set itself - I'm really just not sure what to do with that initial 4.
     
  2. jcsd
  3. Jul 17, 2007 #2

    cepheid

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You have basically solved the problem. The question is, what values of x cause the expression on the left hand side to be zero (i.e. what values of x *satisfy* the equation)? If you ask yourself the question in this way, you will realize that the presence of the additional factor of 4 in front makes NO difference at all. The solution set is still {4,-3}, just as it would be if the 4 were not there. Take a look:

    If x = 4, the expression becomes 4*0*7 = 0
    If x = -3, it becomes 4*(-7)*0 = 0

    Anything multiplied by zero is zero. Therefore, if any ONE of the three factors is zero, the entire product must be zero.
     
  4. Jul 17, 2007 #3

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    If it makes you feel better, you can divide out the factor four.
    You know that performing the same operation on both sides of the equals sign, does not change the equation. Dividing the left hand side by four gives (x - 4)(x + 3). The right hand side gives 0/4 = 0. So the solutions to
    (x - 4)(x + 3) = 0
    are the same as those to
    4 (x - 4)(x + 3) = 0.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Solving for x in a trinomial that has a GCF
  1. Solve for x (Replies: 6)

  2. Solve for (x) (Replies: 3)

  3. Solve for x (Replies: 3)

  4. Solve for x (Replies: 14)

Loading...