If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ;
B) ;
C) ;
D) ;
E) ;

Question

If  is a root of  , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ; 
B) ; 
C) ; 
D) ; 
E) ;

Quizplus · Accepted Answer

We can use synthetic division to factor the polynomial completely as follows:
```
11ec1854_fdd4_e531_acfc_b5704fb991a0_TBX8702_11 | 11ec1854_fdd4_e530_acfc_5b71b6eab3dc_TBX8702_11
---------------------------------------------------
                                                 11ec1854_fdd4_e530_acfc_5b71b6eab3dc_TBX8702_11
```
Therefore, (x - 11ec1854_fdd4_e530_acfc_5b71b6eab3dc_TBX8702_11) is a factor of the polynomial.
Now, to find the other factor, we divide the polynomial by this factor using long division:
```
11ec1854_fdd4_e530_acfc_5b71b6eab3dc_TBX8702_11 | 11ec1854_fdd4_e531_acfc_b5704fb991a0_TBX8702_11 0000000000000000
-------------------------------------------------------------------
                                                 11ec1854_fdd4_e531_acfc_b5704fb991a0_TBX8702_11
                                                - 11ec1854_fdd4_e530_acfc_5b71b6eab3dc_TBX8702_11 0000000000000000
                                                ----------------------------------------------------
                                                  0000000000000000_0000_0000_053c_4ea4f4a4c381_TB
```
Therefore, the other factor is 0000000000000000_0000_0000_053c_4ea4f4a4c381_TB. 
Thus, the fully factored form of the polynomial is (x - 11ec1854_fdd4_e530_acfc_5b71b6eab3dc_TBX8702_11)(0000000000000000_0000_0000_053c_4ea4f4a4c381_TB).
The only real solution to the equation is x = 11ec1854_fdd4_e530_acfc_5b71b6eab3dc_TBX8702_11. Therefore, the correct answer is choice C.

If Is a Root of , Use Synthetic