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'Equating the coefficients' question

  1. Sep 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Expand the brackets to get a cubic containing the unknowns. This is an example in the textbook but I don't see how they've expanded the brackets to get their answer:

    (x-3)(px^2+qx+r)=px^3+(q-3p)x^2+(r-3q)x-3r

    2. Relevant equations
    (x-3)(px^2+qx+r)

    3. The attempt at a solution

    I would have done it how you expand long brackets:

    (x-3)(px^2)+(x-3)(qx)+(x-3)(r)=px^3-3px^2...
     
  2. jcsd
  3. Sep 24, 2016 #2

    pasmith

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    Homework Helper

    Yes, and the next step is to collect all the terms involving x^2 together, and all the terms involving x together...
     
  4. Sep 24, 2016 #3
    What I don't get is how they factorized what you get from expanding: px^3+qx^2+rx-3px^2-3qx-3r. How do you get px^3+(q-3p)x^2+(r-3q)x-3r from that?
     
  5. Sep 24, 2016 #4
    Ah, I see if you do (q-3p)x^2 and multiply it out and the same with the other factorized terms, you get the terms you get when you'd first expand it out. I hadn't noticed that px^3+(q-3p)x^2... etc. was a cubic. I need to work on noticing things, I've found. :rolleyes:
     
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