Use long division to divide. Express any numbers as integers or simplified fractions. \[ \left(-39-19 x-59 x^{2}-4 x^{3}+5 x^{4}\right) \div(x+3)=\square \]

To divide the polynomial \(-39-19x-59x^{2}-4x^{3}+5x^{4}\) by \(x+3\) using long division, let's set it up. 1. First, rewrite the dividend in standard form: \(5x^4 - 4x^3 - 59x^2 - 19x - 39\). 2. Now, divide the leading term \(5x^4\) by the leading term \(x\) of the divisor, which gives us \(5x^3\). 3. Multiply \(5x^3\) by the entire divisor \(x + 3\), resulting in \(5x^4 + 15x^3\). 4. Subtract this from the original polynomial: \[ (5x^4 - 4x^3) - (5x^4 + 15x^3) = -19x^3 \] 5. Bring down the next term \(-59x^2\) to get \(-19x^3 - 59x^2\). 6. Divide \(-19x^3\) by \(x\) to get \(-19x^2\). 7. Multiply \(-19x^2\) by \(x + 3\) to yield \(-19x^3 - 57x^2\). 8. Subtract again to give \(-2x^2 - 19x - 39\). 9. Divide \(-2x^2\) by \(x\) to get \(-2x\). 10. Multiply and subtract, yielding \(+6x - 39\). 11. Divide \(6x\) by \(x\) to get \(6\). 12. Multiply and subtract one last time to arrive at \(-51\). As a result, the quotient is: \[ 5x^3 - 19x^2 - 2x + 6 - \frac{51}{x+3} \] So, the final answer is: \[ 5x^3 - 19x^2 - 2x + 6 - \frac{51}{x+3} \]