1. ## polynomial division

Hi,

Im trying to get my head around how to do polynomial division with undetermined coefficients.

Im trying to divide $\displaystyle z^2-2z+2$
into $\displaystyle z^4-2z^3+az-8z+8$

I run into problems when trying to subtract $\displaystyle 2z^2$ from $\displaystyle az^2$

help appreciated

2. Originally Posted by Jones
Hi,

Im trying to get my head around how to do polynomial division with undetermined coefficients.

Im trying to divide $\displaystyle z^2-2z+2$
into $\displaystyle z^4-2z^3+az-8z+8$

I run into problems when trying to subtract $\displaystyle 2z^2$ from $\displaystyle az^2$

help appreciated

$\displaystyle (z^4-2z^3+az^{\bold{\color{red}2}}-8z+8) \div (z^1-2z+2)$

Use long division:
Code:
(z-1)(2a-12)
z^4-2z^3+az^2-8z+8)÷(z^1-2z+2) = z^2+(a-2) + -----------
z^2-2z+2
-(z^4-2z^3+2z^2)
------------------
(a-2)z^2-8z+8
-((a-2)z^2-2(a-2)z+2(a-2)
--------------------------
-12z+2az-2a+12
The remainder can be factored as shown in the final result.

3. And, specifically, subtracting $\displaystyle 2z^2$ from $\displaystyle az^2$ gives $\displaystyle az^2- 2z^2= (a- 2)z^2$