How to find $\operatorname E(X^2\mid X)$?

Question

I have to find $\operatorname{Var}(Y\mid X)$ where $Y = c + βX$. What I have so far is: \begin{align} \operatorname{Var}(Y\mid X) & = \operatorname E(Y^2\mid X) - \operatorname E(Y\mid X)^2 \\ & = \operatorname E(c^2 + 2c\beta X + (\beta^2)(X^2) \mid X) - (c^2 + 2c\beta X + (\beta^2)(X^2)). \end{align} I know the first part of the last equation is $c^2 + 2cβX + (β^2) \operatorname E(X^2\mid X)$. I'm not sure how to do the $(β^2) \operatorname E(X^2\mid X)$ part.

Answer 1

$$\operatorname{E}[X^2 \mid X] = X^2.$$