Final Answer:
The quotient, without the remainder, for the expression (x^4 + 7x^3 - 11x^2 - 138x - 86)/(x - 4) is x^3 + 11x^2 + 33x + 238.
Step-by-step explanation:
Perform long division by dividing x^4 + 7x^3 - 11x^2 - 138x - 86 by (x - 4).
Identify the term that, when multiplied by (x - 4), results in x^4, which is x^3.
Multiply (x - 4) by x^3 and subtract the result from x^4 + 7x^3 - 11x^2 - 138x - 86.
Bring down the next term, 7x^3, and repeat the process.
Continue this process until all terms are exhausted.
The final quotient, without the remainder, is x^3 + 11x^2 + 33x + 238.