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Math Help - Synthetic Division

  1. #1
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    Synthetic Division

    Use synthetic division to divide

    2x^5 + 3x^4 + 25x^ − 1 by x + 3.

    Also, why call it synthetic?
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  2. #2
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    Quote Originally Posted by symmetry View Post
    Use synthetic division to divide

    2x^5 + 3x^4 + 25x^ − 1 by x + 3.

    Also, why call it synthetic?
    Why is it called synthetic division?
    Umm, maybe because it is not "real" division, it is fake, or "synthetic", division.
    [In building materials, "synthetic" signifies "not natural".]

    [Things like this, definitions, I mean, you can search Google or Wikipedia or Yahoo.]

    It is difficult to show here the form or layout of the synthetic division, but let me try.

    "divide by (x+3)" means (x+3) may be a factor, and so (-3) may be a root, of the expression (2x^5 +3x^4 +25x^2 -1).
    So, (-3) is the first divisor of sort.

    -3...|2.....3.....0.....25.....0.....-1
    ............-6.....9....-27.....6....-18
    ________________________________
    ........2..-3.....9.....-2......6....-19

    It is:
    a) Bring down 2
    b) -3*2 = -6
    c) 3 +(-6) = -3
    d) -3 *(-3) = 9
    e) 0 +9 = 9
    f) -3 *9 = -27
    g) 25 +(-27) = -2
    h) -3 *(-2) = 6
    i) 0 +6 = 6
    j) -3 *6 = -18
    k) -1 +(-18) = -19

    So the quotient is 2x^4 -3x^3 +9x^2 -2x +6, remainder (-19).

    If you studied synthetic division, you may understand the above.
    Not good to explain it here.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    Use synthetic division to divide

    2x^5 + 3x^4 + 25x^ − 1 by x + 3.

    Also, why call it synthetic?
    When I was at school I beleive that we were taught that synthetic division
    was polynimial long division. However this is not the case synthetic division
    is a short cut which is applicable when the divisor is a linear term.

    This site provides more detail.

    RonL
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  4. #4
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    ok

    Thank you both for your effort in terms of synthetic division.

    I will check out purplemath.com.

    I think Elizabeth has a very good site over there.
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