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Simplyfying (Indentitied related)

  1. Aug 30, 2005 #1
    Simple for you guys i guess, But tough for me - Guess im just thick!

    [itex]x^4 +Ax^3 + 5x^2 + x + 3 = (x^2 +4)(X^2 -x +B) +Cx +D[/itex]

    I get:

    [itex]x^4 +Ax^3 + 5x^2 + x + 3 = X^4 -x^3 - 4x^2 + Bx^2 - 4x + 4B + Cx + D[/itex]

    Now, I think i need to simplify this more because i can't compare co-efficients can i?

    Can someone run me through the further simplifications?

    Maybe [itex]Bx^2 + 4x^2[/itex] into [itex](4+B)X^2[/itex] ? Is this wise and possible? What else?

    Need to learn simplification better, Finding my basic maths is poor so Alevel is tough!
     
  2. jcsd
  3. Aug 30, 2005 #2
    The law of distribution of multiplication over addition: a*(b + c) = a*b + a*c. The equality sign means that any expression of the form of the right hand side may be replaced by the expression on the left hand side (and vice versa) and still maintain the truth of the original expression. As long as X=x in your expression, what you're doing is fine. :smile:
     
  4. Aug 30, 2005 #3
    You're on the right path, my friend!

    [tex]x^4 +Ax^3 + 5x^2 + x + 3 = (x^2 +4)(x^2 -x +B) +Cx +D[/tex]
    <=>
    [tex]x^4 +Ax^3 + 5x^2 + x + 3 = x^4 - x^3 + Bx^2 + 4x^2 - 4x + 4B +Cx +D[/tex]
    <=(cancellation & simplification)=>
    [tex]Ax^3 + 5x^2 + x + 3 = - x^3 + (B+4)x^2 + (C-4)x + 4B + D[/tex]
     
  5. Aug 30, 2005 #4

    HallsofIvy

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    Now recall that if that is true for all x, then the corresponding coefficients must be equal. You can just look at that and see what A must be!
     
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