# synthetic division

• May 17th 2008, 09:26 AM
afeasfaerw23231233
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
• May 17th 2008, 09:35 AM
Mathstud28
Quote:

Originally Posted by afeasfaerw23231233
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 $x^4-2x+5=x^4+0x^3+0x^2-2x+5$
• May 17th 2008, 09:57 AM
afeasfaerw23231233
thanks but can i divide a polynomial f(x) by a non-monic polynomial g(x) unless change it's form? for example : $f(x) = 3x^5+9x^4-5x^3 +8x^2-4x+3
g(x) = 5x^3+4x^2-3x+9$

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?
• May 17th 2008, 09:59 AM
earboth
Quote:

Originally Posted by afeasfaerw23231233
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.
• May 18th 2008, 10:27 PM
afeasfaerw23231233
my textbook never says anything about Synthetic Division :(