Algebra Question(Part of a Larger Problem)

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In summary, the conversation is about a request for help in simplifying the expression f(x) = (2x)(x-5)^(3) + 3x^2(x-5)^(2). The back of the book provides the solution of 5x(x-5)^(2)(x-2). The person seeking help was advised to factor out the common term of x*(x-5)^2 which would leave 2(x-5) + (3x+1). After realizing their mistake, they were able to solve the problem.
  • #1
undrcvrbro
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Homework Statement


f(x) = (2x)(x-5)^(3) + 3x^2(x-5)^(2)

Need to simplify.


Homework Equations





The Attempt at a Solution


I tried simplifying completely but my answer wasn't even close. The Back of the book has:
5x(x-5)^(2)(x-2)

I know its easy, but I'm drawing a blank...can anyone start me off on the right path to find how they got that answer?
 
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  • #2
The first thing to notice is that both terms in your expression have a common factor of x*(x-5)^2. Factor that out. Now what's left in each term?
 
  • #3
Well, wouldn't it then be 2(x-5) + (3x+1)?
 
  • #4
I get just 2(x-5)+3x. Where did the 1 come from?
 
  • #5
Oh! I got it!

Oh wow. I can't believe I had made a mistake like that. Thank you so much. I just figured it out.

Thanks Dick.
 

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