Answer :
Final answer:
The quotient in the polynomial form for the synthetic division problem 2 | 1 7 -18 is D. x + 9. The process involves carrying down and combining coefficients systematically.
Explanation:
To solve the synthetic division problem given as 2 | 1 7 -18, we follow these steps:
- Bring down the initial coefficient, 1, to the bottom row.
- Multiply this coefficient by 2 (the divisor), and place the result (2) under the next coefficient (7).
- Add the numbers in the second column to get the new coefficient (7 + 2 = 9).
- Multiply the new coefficient by the divisor (9 * 2 = 18) and place this result under the -18.
- Add the last column to get the new last coefficient (-18 + 18 = 0).
- The numbers in the bottom row represent the coefficients of the quotient polynomial. In this case, the coefficients are 1 and 9.
The quotient in polynomial form of the division is x + 9, so the correct answer is D. x + 9.
Always remember to eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable.
