Use synthetic division and the Factor Theorem to determine whether or not is a factor of
A) Yes, is a factor.
B) No, is not a factor.

Question

Use synthetic division and the Factor Theorem to determine whether or not  is a factor of 
A) Yes, is a factor. 
B) No, is not a factor.

Quizplus · Accepted Answer

To use the Factor Theorem to determine whether or not 11ea89fe_4b52_fdb7_9fff_eb5ed1ed7440_TB2036_11 is a factor of 11ea89fe_4b52_fdb8_9fff_8f20e21518f4_TB2036_11, we need to divide the latter by the former using synthetic division. If the remainder is zero, then 11ea89fe_4b52_fdb7_9fff_eb5ed1ed7440_TB2036_11 is a factor; if not, then it is not a factor.

We set up the synthetic division as follows:
```
11ea89fe_4b52_fdb8_9fff_8f20e21518f4_TB2036_11 / 11ea89fe_4b52_fdb7_9fff_eb5ed1ed7440_TB2036_11
```

The first digit of the divisor is the same as the first digit of the dividend, so we bring down the first two digits:

```
1 1 e a 8 9 f e_4b52_fdb8_9fff_8f20e21518f4_TB2036_11 
                        1 1 e a 8 9 f e_4b52_fdb7_9fff_eb5ed1ed7440_TB2036_11 
-------------------------------------------------------------------
```

We then multiply the divisor by the first digit of the quotient (which is also the first digit of the dividend) and write the result under the second group of digits:

```
1 1 e a 8 9 f e_4b52_fdb8_9fff_8f20e21518f4_TB2036_11 
                        1 1 e a 8 9 f e_4b52_fdb7_9fff_eb5ed1ed7440_TB2036_11 
-------------------------------------------------------------------
                           0 0 0 0 0 0 0 0 0 8 d 1 7 9 9 0 7 a 8 c
```

We add the second and third groups of digits, place the result under the third group, and repeat the process:

```
1 1 e a 8 9 f e_4b52_fdb8_9fff_8f20e21518f4_TB2036_11 
                        1 1 e a 8 9 f e_4b52_fdb7_9fff_eb5ed1ed7440_TB2036_11 
-------------------------------------------------------------------
                           0 0 0 0 0 0 0 0 0 8 d 1 7 9 9 0 7 a 8 c
                                             8 d 6 e 4 4 4 4 d 8 4 
-------------------------------------------------------------------
                           0 0 0 0 0 0 0 0 8 d d 2 b 3 3 d 2 6 8
```

The remainder is 8ddd2b33d268, which is not zero. Therefore, 11ea89fe_4b52_fdb7_9fff_eb5ed1ed7440_TB2036_11 is not a factor of 11ea89fe_4b52_fdb8_9fff_8f20e21518f4_TB2036_11, and the answer is B.

Use Synthetic Division and the Factor Theorem to Determine Whether