The revenue function of a company that sells gaming consoles is R(x) = 6x2 + 100x + 300. The cost function is C(x) = 25x + 100. Which function describes the profit function of the company?

To find the profit function \( P(x) \) of the company, we use the formula: \[ P(x) = R(x) - C(x) \] where \( R(x) \) is the revenue function and \( C(x) \) is the cost function. Given: \[ R(x) = 6x^2 + 100x + 300 \] \[ C(x) = 25x + 100 \] Now, we can substitute \( R(x) \) and \( C(x) \) into the profit function formula: \[ P(x) = (6x^2 + 100x + 300) - (25x + 100) \] Simplifying this, we distribute the negative sign across \( C(x) \): \[ P(x) = 6x^2 + 100x + 300 - 25x - 100 \] Now, combine like terms: \[ P(x) = 6x^2 + (100x - 25x) + (300 - 100) \] \[ P(x) = 6x^2 + 75x + 200 \] Thus, the profit function \( P(x) \) is: \[ P(x) = 6x^2 + 75x + 200 \]