Divide. \[ \left(15 x^{2}-29 x\right) \div(5 x-8) \] \( \square \)

To divide the polynomial \(15x^2 - 29x\) by \(5x - 8\), we can use polynomial long division. 1. Divide the leading term of the numerator \(15x^2\) by the leading term of the denominator \(5x\) to get \(3x\). 2. Multiply \(3x\) by the entire divisor \(5x - 8\), resulting in \(15x^2 - 24x\). 3. Subtract this product from the original polynomial: \[ (15x^2 - 29x) - (15x^2 - 24x) = -5x \] 4. Now, bring down the next term (if there were any), but since we only have a single term left, now we divide \(-5x\) by \(5x - 8\). 5. \(-5x\) divided by \(5x\) gives \(-1\). 6. Multiply \(-1\) by \(5x - 8\), giving \(-5x + 8\). 7. Subtract it from \(-5x\): \[ -5x - (-5x + 8) = 8 \] So, the result of the division can be expressed as: \[ 3x - 1 + \frac{8}{5x - 8} \] Thus, the final answer is: \[ 3x - 1 + \frac{8}{5x - 8} \]