\( (x+3)\left(2 x-\frac{1}{3}\right) \) What is the product? A \( \quad 2 x^{2}-1 \) B \( \quad 2 x^{2}+1 \) C \( \quad 2 x^{2}+\frac{17 x}{3}-1 \) D \( \quad 2 x^{2}+\frac{19 x}{3}-1 \)

To find the product of \( (x+3)\left(2 x-\frac{1}{3}\right) \), we can use the distributive property (also known as the FOIL method for binomials). First, distribute \( x \) from the first term to both terms in the second term: \( x \cdot 2x - x \cdot \frac{1}{3} = 2x^2 - \frac{x}{3} \). Next, distribute \( 3 \) from the first term to both terms in the second term: \( 3 \cdot 2x - 3 \cdot \frac{1}{3} = 6x - 1 \). Now, combine all the results: \( 2x^2 - \frac{x}{3} + 6x - 1 \). To combine the like terms, we convert \( 6x \) into thirds: \( 6x = \frac{18x}{3} \), so we have: \( 2x^2 + \left(-\frac{x}{3} + \frac{18x}{3}\right) - 1 = 2x^2 + \frac{17x}{3} - 1 \). The correct product is \( C \quad 2 x^{2}+\frac{17 x}{3}-1 \).