Multiply the following and collect like terms: \[ (2 x+3) \cdot\left(-3 x^{2}-2 x+3\right) \] Select the correct answer below: \( -6 x^{3}-13 x^{2}+12 x+9 \) \( -6 x^{3}-13 x^{2}-12 x+9 \) \( -6 x^{3}-6 x^{2}-6 x+9 \) \( -6 x^{3}-13 x^{2}+9 \) \( -6 x^{3}-6 x^{2}+9 \)

We start by expanding the product: \[ (2x+3) \cdot \left(-3x^2-2x+3\right) \] Distribute each term of \((2x+3)\) over the second polynomial: 1. Multiply \(2x\) by each term: \[ 2x \cdot (-3x^2) = -6x^3 \] \[ 2x \cdot (-2x) = -4x^2 \] \[ 2x \cdot 3 = 6x \] 2. Multiply \(3\) by each term: \[ 3 \cdot (-3x^2) = -9x^2 \] \[ 3 \cdot (-2x) = -6x \] \[ 3 \cdot 3 = 9 \] Now, combine like terms: - For \(x^3\): \[ -6x^3 \] - For \(x^2\): \[ -4x^2 - 9x^2 = -13x^2 \] - For \(x\): \[ 6x - 6x = 0x \] - Constant term: \[ 9 \] Thus, the simplified expression is: \[ -6x^3 - 13x^2 + 9 \] Comparing with the provided options, the correct answer is: \[ -6x^3 - 13x^2 + 9 \]