Perform the division. (Simplify your answer completely.) \[ \left(x^{2}+6 x+14\right) \div(x+5) \] SUBMIT ANSWER

To perform the division of \( \left(x^{2}+6x+14\right) \) by \( (x+5) \), we can use polynomial long division. 1. Divide the leading term: \( x^2 \div x = x \). 2. Multiply the entire divisor \( (x + 5) \) by \( x \): \( x(x+5) = x^2 + 5x \). 3. Subtract this from the original polynomial: \[ (x^2 + 6x + 14) - (x^2 + 5x) = (6x - 5x) + 14 = x + 14. \] 4. Bring down the next term to get \( (x + 14) \) . 5. Now, divide the leading term again: \( x \div x = 1 \). 6. Multiply the entire divisor \( (x + 5) \) by \( 1 \): \( 1(x+5) = x + 5 \). 7. Subtract again: \[ (x + 14) - (x + 5) = 14 - 5 = 9. \] This leaves us with a remainder of \( 9 \). Putting it all together, we have: \[ \frac{x^2 + 6x + 14}{x + 5} = x + 1 + \frac{9}{x + 5}. \] So the simplified answer is: \[ x + 1 + \frac{9}{x + 5}. \]