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`