Let's solve the expression $2 + x^2 \cdot 5$ when $x = 3$.

Step-by-step process:

1. Substitute $x = 3$ into the expression: $2 + (3^2) \cdot 5$

2. Calculate $3^2$: $3^2 = 9$ So the expression becomes: $2 + 9 \cdot 5$

3. Now multiply $9 \cdot 5$: $9 \cdot 5 = 45$

4. Finally, add $2 + 45$: $2 + 45 = 47$

Thus, the value of the expression is 47, which corresponds to option C.

Would you like any more details on this solution?

Here are 5 related questions:

1. How would the result change if $x = 4$?
2. What happens to the expression if the coefficient of $x^2$ is changed to 6?
3. Can you expand the expression $2 + x^2 \cdot 5$ for $x = -3$?
4. How would you solve a similar expression, $3 + x^3 \cdot 2$, for $x = 2$?
5. What is the general form of this expression if $x$ is a variable?

Tip: When solving expressions, always remember to follow the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).