Find the product. \( (5 x-2)\left(x^{2}-3 x+1\right) \) \( (5 x-2)\left(x^{2}-3 x+1\right)=\square \)

1. Write the product: \[ (5x-2)(x^2-3x+1) \] 2. Distribute the term \(5x\) over the trinomial: \[ 5x \cdot x^2 = 5x^3 \] \[ 5x \cdot (-3x) = -15x^2 \] \[ 5x \cdot 1 = 5x \] 3. Distribute the term \(-2\) over the trinomial: \[ -2 \cdot x^2 = -2x^2 \] \[ -2 \cdot (-3x) = 6x \] \[ -2 \cdot 1 = -2 \] 4. Combine like terms: - Combine the \(x^3\) term: \(5x^3\) - Combine the \(x^2\) terms: \(-15x^2 - 2x^2 = -17x^2\) - Combine the \(x\) terms: \(5x + 6x = 11x\) - Constant term: \(-2\) This gives: \[ 5x^3 - 17x^2 + 11x - 2 \] 5. Therefore, the product is: \[ (5x-2)(x^2-3x+1)=5x^3 - 17x^2 + 11x - 2 \]