Compute the following product. \[ (5 x-2)(x+1) \]

To compute the product \((5x-2)(x+1)\), we can use the distributive property (also known as the FOIL method for binomials). We multiply each term in the first binomial by each term in the second binomial: 1. First: \(5x \cdot x = 5x^2\) 2. Outer: \(5x \cdot 1 = 5x\) 3. Inner: \(-2 \cdot x = -2x\) 4. Last: \(-2 \cdot 1 = -2\) Now, we combine these results: \[ 5x^2 + 5x - 2x - 2 \] Combining the like terms \(5x\) and \(-2x\): \[ 5x^2 + (5x - 2x) - 2 = 5x^2 + 3x - 2 \] Therefore, the product is: \[ \boxed{5x^2 + 3x - 2} \]