## Algebra 1

$$c^2-\frac{1}{c-1}$$
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. $$c^2-\frac{1}{c-1}$$