Answer
$$c^2-\frac{1}{c-1}$$
Work Step by Step
In order to divide a polynomial by a bionomial, there must be a term for every power between the highest power and zero. To do this, add a placeholder of $0c$
$$(c^3-c^2+0c-1)\div(c-1)$$
Multiply by $c^2$ to match the first term of the dividend. The $c^2$ will go on top of your division sign
$$(c^2)(c-1)=c^3-c^2$$
Subtract this from the dividend
$$(c^3-c^2+0c-1)-(c^3-c^2)=0c^2$$
Bring down the next term of the dividend
$$0c^2+0c$$
Multiply by $0c$ to match this. The $0c$ can follow $c^2$ in your work, but it will not be in the final answer.
$$(0c)(c-1)=0c^2-0c$$
Subtract this from the dividend
$$(0c^2+0c)-(oc^2+0c)=0c$$
Bring down the next term of the dividend
$$0c-1$$
Multiply by $0$ to match this. The $0$ can go on top of your division sign in your work, but it will not be in the final answer.
$$(0)(c-1)=0c-0$$
Subtract this from the dividend
$$(0c-1)-(0c-0)=-1$$
Since your remainder is $-1$, you can add $\frac{-1}{c-1}$ to your answer.
$$c^2-\frac{1}{c-1}$$
