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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).

What is the value of the expression 2 + x^2 * 5 when x = 3?

Learn how to solve the expression 2 + x^2 * 5 when x = 3. This problem covers key algebra concepts, including exponents and order of operations. Suitable for students in Grades 6-8.

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