High School

Complete the synthetic division problem below:

2 | 1 7 -18

What is the quotient in polynomial form?

A. x - 7
B. x - 9
C. x + 7
D. x + 9

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:

  1. Bring down the initial coefficient, 1, to the bottom row.
  2. Multiply this coefficient by 2 (the divisor), and place the result (2) under the next coefficient (7).
  3. Add the numbers in the second column to get the new coefficient (7 + 2 = 9).
  4. Multiply the new coefficient by the divisor (9 * 2 = 18) and place this result under the -18.
  5. Add the last column to get the new last coefficient (-18 + 18 = 0).
  6. 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.