Final Answer:
The remainder of the quotient of the polynomial divided by (x - a) is 17.
Step-by-step explanation:
Braulio and Zahra used different methods to find the value of a in the given polynomial. Braulio employed synthetic division, while Zahra applied the remainder theorem.
Braulio's synthetic division involves dividing the polynomial by (x - a) and finding the remainder. Let's denote the polynomial as P(x). The synthetic division can be expressed as P(a) = 17, where P(a) represents the remainder when the polynomial is divided by (x - a). Therefore, the remainder of the quotient is indeed 17, as stated in the final answer.
Zahra, on the other hand, utilized the remainder theorem, which states that if you divide a polynomial P(x) by (x - a), the remainder is P(a). In this scenario, the remainder is again 17, consistent with Braulio's result. Both methods converge on the same conclusion, confirming that the remainder of the quotient of the polynomial divided by (x - a) is indeed 17. This reinforces the accuracy of the answer provided in the first part.
In summary, Braulio and Zahra's independent approaches lead to the same outcome: the remainder when the polynomial is divided by (x - a) is 17. This not only affirms the validity of the answer but also showcases the versatility and reliability of different mathematical methods in reaching a common solution.