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A division and a problem

  1. May 15, 2010 #1
    1. The problem statement, all variables and given/known data
    I forgot how to divide this

    1.) x^2 + 15 -8x divided by 3 - x

    I dont know how to start since 3 has nothing to do with x^2.
    The result from the book is 5 - x.


    I also dont understand this problem which uses trigonometric identities.
    if x = a sin theta then

    2.) square rt of a^2 - x^2

    = square rt of a^2 - a^2 sin^2 theta
    = square rt of a^2 square rt of 1 - sin^2 theta
    = a cos theta .

    I dont understand why does

    square rt of a^2 - a^2 sin^2 theta

    = square rt of a^2 square rt of 1 - sin^2 theta ?



    2. Relevant equations



    3. The attempt at a solution

    Thanks in advance.
     
  2. jcsd
  3. May 15, 2010 #2

    Gib Z

    User Avatar
    Homework Helper

    1) When dividing, rewrite all the polynomials with highest power of x first, then decreasing powers of x from there.

    2) Firstly, we can factor a^2-a^2 sin^2 theta as a^2( 1 - sin^2 theta).

    Then we can break up the squareroot using [itex]\sqrt{xy} = \sqrt{x} \sqrt{y}[/itex].
     
  4. May 15, 2010 #3
  5. May 15, 2010 #4
    Thanks by ordering the polynomials and using syntethic division I have 3 dividing 1 -8 +15 which equals x - 5 ?
     
  6. May 16, 2010 #5

    Mark44

    Staff: Mentor

    No. Dividing x2 - 8x + 15 by 3 - x is equivalent to dividing -x2 + 8x - 15 by x - 3.
     
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