Which experssion is equal to \( (x+5)\left(-3 x^{2}+15 x-1\right) \) \( \begin{array}{l}-3 x^{3}+74 x-5 \\ -3 x^{3}-76 x-5 \\ -3 x^{3}+30 x^{2}-76 x-5 \\ -3 x^{3}+30 x^{2}+74 x-5\end{array} \)

To simplify the expression \( (x+5)\left(-3 x^{2}+15 x-1\right) \), we can use the distributive property (also called the FOIL method for binomials). Let's distribute \( x \) and \( 5 \) through \(-3x^2 + 15x - 1\): 1. \( x \cdot (-3x^2) = -3x^3 \) 2. \( x \cdot 15x = 15x^2 \) 3. \( x \cdot (-1) = -x \) Now for \( 5 \): 1. \( 5 \cdot (-3x^2) = -15x^2 \) 2. \( 5 \cdot 15x = 75x \) 3. \( 5 \cdot (-1) = -5 \) Now combine all the results: - From \( x \): \( -3x^3 + 15x^2 - x \) - From \( 5 \): \( -15x^2 + 75x - 5 \) Combine like terms: - The \( x^2 \) terms: \( 15x^2 - 15x^2 = 0 \) - The \( x \) terms: \( -x + 75x = 74x \) So, the final combined expression is: \[ -3x^3 + 74x - 5 \] Therefore, the answer is \( -3x^3 + 74x - 5 \).