What is the remainder when 3 is synthetically divided into the polynomial -x2 + 5x - 9?A.0B.-6C.-3D.5SUBMITarrow_backPREVIOUS

To solve this problem, we will use synthetic division. Here are the steps:

1. Write down the coefficients of the polynomial. For -x^2 + 5x - 9, the coefficients are -1, 5, and -9.

2. Write down the number you are dividing by, which is 3, to the left of a vertical line. To the right of this line, write down the coefficients from step 1.

3. Bring down the first coefficient (-1) to the bottom row.

4. Multiply the number you just wrote down by the number you are dividing by (3). Write this result (-3) under the second coefficient (5).

5. Add the numbers in this column together (5 + -3 = 2) and write the result in the bottom row.

6. Repeat steps 4 and 5 for the rest of the coefficients. Multiply 2 (the number you just wrote down) by 3 (the number you are dividing by) to get 6. Write this under the next coefficient (-9). Add these together to get -3.

So, the remainder when 3 is synthetically divided into the polynomial -x^2 + 5x - 9 is -3. Therefore, the answer is C. -3.