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Math Help - synthetic division

  1. #1
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    synthetic division

    i've just read a page in wikipedia about synthetic division Polynomial long division - Wikipedia, the free encyclopedia
    i find it interesting and helpful.
    but can i do a synthetic division if a polynomial is divided by a non-monic polynomial such as 3x^2+2x+5 ? thanks
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by afeasfaerw23231233 View Post
    i've just read a page in wikipedia about synthetic division Polynomial long division - Wikipedia, the free encyclopedia
    i find it interesting and helpful.
    but can i do a synthetic division if a polynomial is divided by a non-monic polynomial such as 3x^2+2x+5 ? thanks
    Yes you can....it does not matter what the coeficients are for the polynomial..

    Synthetic Division -- from Wolfram MathWorld

    Remember x^4-2x+5=x^4+0x^3+0x^2-2x+5
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    thanks but can i divide a polynomial f(x) by a non-monic polynomial g(x) unless change it's form? for example : f(x) = 3x^5+9x^4-5x^3 +8x^2-4x+3 <br />
g(x) = 5x^3+4x^2-3x+9
    can i divide f(x) by g(x) using synthetic division directly without changing
     \frac {3x^5+9x^4-5x^3 +8x^2-4x+3}{5x^3+4x^2-3x+9} to
     \frac {\frac 3 5 x^5+\frac 9 5 x^4-x^3 +\frac 8 5 x^2- \frac  4 5 x+\frac  3 5}{x^3+\frac 4 5 x^2-\frac 3 5 x+\frac 9 5}
    since g(x) isn't a monic polynomial?
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  4. #4
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    Quote Originally Posted by afeasfaerw23231233 View Post
    i've just read a page in wikipedia about synthetic division Polynomial long division - Wikipedia, the free encyclopedia
    i find it interesting and helpful.
    but can i do a synthetic division if a polynomial is divided by a non-monic polynomial such as 3x^2+2x+5 ? thanks
    1. With synthetic division the divisor must be a linear and monic term.

    2. If the divisor is a non-monic linear term divide the complete quotient by the leading coefficient of the divisor to change it into a monic linear term.

    Example: (7x^5-3x^4+x-6) \div (3x+4) = \left(\frac73 x^5-x^4+\frac13 x - 2  \right) \div \left(x+\frac43  \right)

    3. If the divisor isn't linear you have to use long division.
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  5. #5
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    my textbook never says anything about Synthetic Division
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