Question

Complete the synthetic division problem below:

2 | 1 7 -18
What is the quotient in polynomial form?

a) 1x^2 + 9x + 18
b) x^2 + 7x - 9
c) x^2 + 3x - 9
d) 1x^2 + 3x - 9

Answer 1

Synthetic division of the given expression results in the quotient x^2 + 9x; however, among the provided options, none match exactly. The closest option with a potential typo is b) x^2 + 7x - 9, but the correct answer should be x^2 + 9x.

Step-by-step explanation:

We are asked to complete a synthetic division and provide the quotient in polynomial form. The setup is 2 | 1 7 -18. Here's how we complete the synthetic division step by step:

1. Bring down the leading coefficient, which is 1, to the bottom row.
2. Multiply 2 by the number at the bottom (initialized as 1), which gives you 2, and write this number underneath the second coefficient (7), then sum the two numbers getting 9. The new row now is 1 and 9.
3. Repeat the process multiplying 2 by the new number at the bottom (9) to obtain 18, add this to the third number (-18), resulting in 0. The new row is now 1, 9, 0.

The bottom row numbers represent the coefficients of the quotient polynomial. So, the quotient is x^2 + 9x + 0 or simplified as x^2 + 9x.

Thus, among the provided options, none match exactly, but the closest option without the error term would be b) x^2 + 7x - 9 if we consider it a typo, since the remainder is 0, not -9. The correct quotient should be x^2 + 9x.