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January 3rd, 2016, 06:54 PM  #1 
Newbie Joined: Sep 2014 From: USA Posts: 6 Thanks: 0  Product of Linear Factors
Problem: Rewrite (4x^2+5x)^2  5(4x^2+5x)  6 as a product of linear factors. I have no idea where to start. I tried using the substitution method to get (4x^2 + 5x  6)(4x^2 + 5x + 1) and using the quadratic formula to get x = 3/4, 2, 1, and 1/4. Last edited by skipjack; January 3rd, 2016 at 07:34 PM. 
January 3rd, 2016, 07:08 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond 
That's a good approach. If you've got x = 3/4, then 4x  3 = 0. (4x  3)(x + 2)(4x + 1)(x + 1) is equivalent to the original expression. Last edited by skipjack; January 3rd, 2016 at 07:29 PM. 
January 3rd, 2016, 07:16 PM  #3  
Newbie Joined: Sep 2014 From: USA Posts: 6 Thanks: 0  Quote:
I overlooked 4x  3 = 0 and used x = 3/4 instead. Last edited by skipjack; January 3rd, 2016 at 07:30 PM.  

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