To solve the expression $(C - p)(x) = (5x^2 + 17x - 12) - (x - 2)$, we'll follow these steps:

1. Distribute the negative sign across the terms in the second expression $(x - 2)$.
2. Combine like terms to simplify the expression.

Let's go through the process step by step:

Step 1: Distribute the negative sign

$(C - p)(x) = (5x^2 + 17x - 12) - x + 2$

Step 2: Combine like terms

Now, combine the terms that involve $x$ and the constant terms:

$(C - p)(x) = 5x^2 + 17x - x - 12 + 2$ $(C - p)(x) = 5x^2 + (17x - x) + (-12 + 2)$ $(C - p)(x) = 5x^2 + 16x - 10$

So, the simplified expression is:

$(C - p)(x) = 5x^2 + 16x - 10$

This is the final simplified form of the expression.

Would you like more details or have any other questions?

Related Questions:

1. How would you solve the equation $5x^2 + 16x - 10 = 0$?
2. What happens if you change the constant terms in the original expression?
3. Can you express $(C - p)(x)$ in a different form by factoring?
4. How does the expression change if the coefficient of $x^2$ was different?
5. What are the roots of the quadratic expression $5x^2 + 16x - 10$?

Tip:

When simplifying expressions, always ensure you distribute negative signs carefully to avoid errors.