If $x = -3$, then $x^3 - x^2 - x$ will be equal to

### Concept & Formula This is a direct polynomial evaluation problem. The goal is to substitute a specific value into an algebraic expression and calculate the result. The core concept tested is the rule of signs for exponents: * A negative base raised to an **odd** power results in a **negative** number. * A negative base raised to an **even** power results in a **positive** number. ### Step-by-Step Solution Given the expression: $$x^3 - x^2 - x$$ * **Step 1: Substitute the value** Replace every instance of $x$ with $(-3)$. Use parentheses to avoid sign errors: $$(-3)^3 - (-3)^2 - (-3)$$ * **Step 2: Evaluate the Exponents** Calculate the cube: $(-3)^3 = -3 \times -3 \times -3 = -27$ Calculate the square: $(-3)^2 = -3 \times -3 = 9$ * **Step 3: Rewrite the expression** Substitute the expanded values back into the equation: $$-27 - (9) - (-3)$$ * **Step 4: Resolve the signs and compute** Subtracting a negative is the same as addition: $$-27 - 9 + 3$$ $$-36 + 3 = -33$$ ### Exam Strategy & Shortcut When substituting negative values, immediately write down the expected sign for each term before doing the multiplication. Term 1 ($x^3$): Negative Term 2 ($-x^2$): Negative (because $x^2$ is positive, but it's subtracted) Term 3 ($-x$): Positive (double negative) This mental check confirms the structure is $- A - B + C$, heavily minimizing careless sign-flipping mistakes under pressure. ### Common Pitfall A very common mistake is improperly evaluating $-x^2$. Students often write $-(-3)^2 = +9$, erroneously multiplying the outer negative by the inner negative before squaring. Exponents must always be resolved before the subtraction operator is applied outside. ### Final Answer **Therefore, the correct answer is -33.**