Given the Synthetic Division shown in the exercise, you can find the Quotient as follows:
1. Write down the first coefficient below the horizontal line:
2. Multiply the coefficient by -1 (the number on the left):
[tex](1)(-1)=-1[/tex]
3. Write the result obtained below the second coefficient (in this case this is 7) and add them (write the sum below the horizontal line).
Then:
4. Multiply the number -1 on the left of the box by the Sum obtained:
[tex](-1)(6)=-6[/tex]
5. Write the Product below the third coefficient and add them.
6. Write the sum below the horizontal line.
Then:
7. Multiply the number -1 by the Sum 9:
[tex](-1)(9)=-9[/tex]
8. Write the Product below the last coefficient and add them.
9. Write the sum below the horizontal line.
Then:
As you can notice, you obtained these coefficients of the Quotient:
[tex]1,6,9[/tex]
These are the coefficients of the new polynomial. Therefore, you get that this has this form:
[tex]x^2+6x+9[/tex]
Hence, the answer is: Option A.
