Thread: 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 ? thanks

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 ? thanks

Yes you can....it does not matter what the coeficients are for the polynomial..

Synthetic Division -- from Wolfram MathWorld

Remember

thanks but can i divide a polynomial f(x) by a non-monic polynomial g(x) unless change it's form? for example :
can i divide f(x) by g(x) using synthetic division directly without changing
to

since g(x) isn't a monic polynomial?

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 ? 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:

3. If the divisor isn't linear you have to use long division.

my textbook never says anything about Synthetic Division