To evaluate \( 2x^3 - 7x^2 - 3x + 22 \) when \( x = -3 \), substitute \( -3 \) for \( x \) in the equation:

\[
2(-3)^3 - 7(-3)^2 - 3(-3) + 22
\]

Now, calculate each term:

1. \( 2(-3)^3 = 2(-27) = -54 \)
2. \( -7(-3)^2 = -7(9) = -63 \)
3. \( -3(-3) = 9 \)
4. The constant is \( 22 \).

Now, sum them up:

\[
-54 - 63 + 9 + 22 = -86
\]

Thus, the value of the expression when \( x = -3 \) is **-86**.

Would you like more details or have any questions about this? 

Here are 5 related questions to consider:

1. What happens if you change the coefficient of \( x^3 \) to another number?
2. Can you factor the polynomial \( 2x^3 - 7x^2 - 3x + 22 \)?
3. How would this polynomial behave graphically at \( x = -3 \)?
4. What is the derivative of \( 2x^3 - 7x^2 - 3x + 22 \)?
5. Can you solve for \( x \) when this polynomial equals zero?

**Tip:** Always substitute values carefully, keeping track of negative signs to avoid errors.

Learn how to evaluate the polynomial 2x^3 - 7x^2 - 3x + 22 when x = -3 with a detailed, step-by-step solution. This example demonstrates key concepts in algebra, including substitution and polynomial evaluation. Perfect for students in Grades 9-12 looking to strengthen their understanding of polynomial expressions.

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