Question

Dividing polynomials
$( {z}^{4} - {3z}^{3 } + {2z}^{2} - 4z + 4)(z - 1) ^{ - 1}$
how do you simplify this????

Answer 1

$z^4-3z^3+2z^2-4z+4=\\\\z^4-z^3-2z^3+2z^2-4z+4=\\\\z^3(z-1)-2z^2(z-1)-4(z-1)=\\\\(z^3-2z^2-4)(z-1)$

So

$(z^4-3z^3+2z^2-4z+4)(z-1)^{-1}=z^3-2z^2-4$