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Answer :
The quotient polynomial is x + 7. Hence the correct option is a.
1. Set up the synthetic division problem:
2 | 1 5 -14
------------------
↓
2. Bring down the first coefficient:
2 | 1 5 -14
------------------
↓
1
3. Multiply the divisor (2) by the number just brought down (1), and place the product under the next coefficient:
2 | 1 5 -14
------------------
↓ 2
1
4. Add the numbers in the second column:
2 | 1 5 -14
------------------
↓ 2
1 7
5. Repeat steps 3 and 4 for the remaining columns:
2 | 1 5 -14
------------------
↓ 2 14
1 7 0
6. The numbers in the bottom row are the coefficients of the quotient polynomial:
1 7 0
Therefore, the quotient polynomial is x + 7, which corresponds to option A.
Complete question:
Complete the synthetic division problem below.
2/ (1x² + 5x - 14)
What is the quotient in polynomial form?
A. X+7
B. X-5
C. x+ 5
D. X-7
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