polynomial division

Hi,

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

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

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

help appreciated

Quote:

Originally Posted by Jones

Hi,

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

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

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

help appreciated

According to your explanations I assume that the quotient reads:

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

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.

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