Using synthetic division (Ruffini's Rule), perform the following division:

3x^{4} + 6x^{3} - 123x^{2} - 126x + 1080 | |

x - 5 |

__Determine our root divisor:__ To find our root, we solve the divisor equation x - 5 = 0

We add 5 to each side of the equation to get x - 5 + 5 = 0 + 5

Therefore, our root becomes x = 5

__Step 1: Write down our coefficients horizontally and our root of 5 to the left:__ __Step 2: Bring down the first coefficient of __**3** __Step 3: Multiply our root of __**5** by our last result of **3** to get **15** and put that in column 2: | 3 | 6 | -123 | -126 | 1080 |

**5** | | ** 15** | | | |

| ** 3** | | | | |

__Step 4: Add the new entry of __**15** to our coefficient of **6** to get **21** and put this in the answer column 2: | 3 | ** 6** | -123 | -126 | 1080 |

5 | | ** 15** | | | |

| 3 | ** 21** | | | |

__Step 5: Multiply our root of __**5** by our last result of **21** to get **105** and put that in column 3: | 3 | 6 | -123 | -126 | 1080 |

**5** | | 15 | ** 105** | | |

| 3 | ** 21** | | | |

__Step 6: Add the new entry of __**105** to our coefficient of **-123** to get **-18** and put this in the answer column 3: | 3 | 6 | ** -123** | -126 | 1080 |

5 | | 15 | ** 105** | | |

| 3 | 21 | ** -18** | | |

__Step 7: Multiply our root of __**5** by our last result of **-18** to get **-90** and put that in column 4: | 3 | 6 | -123 | -126 | 1080 |

**5** | | 15 | 105 | ** -90** | |

| 3 | 21 | ** -18** | | |

__Step 8: Add the new entry of __**-90** to our coefficient of **-126** to get **-216** and put this in the answer column 4: | 3 | 6 | -123 | ** -126** | 1080 |

5 | | 15 | 105 | ** -90** | |

| 3 | 21 | -18 | ** -216** | |

__Step 9: Multiply our root of __**5** by our last result of **-216** to get **-1080** and put that in column 5: | 3 | 6 | -123 | -126 | 1080 |

**5** | | 15 | 105 | -90 | ** -1080** |

| 3 | 21 | -18 | ** -216** | |

__Step 10: Add the new entry of __**-1080** to our coefficient of **1080** to get **0** and put this in the answer column 5: | 3 | 6 | -123 | -126 | ** 1080** |

5 | | 15 | 105 | -90 | ** -1080** |

| 3 | 21 | -18 | -216 | ** 0** |

Our synthetic division is complete. The values in our results row form a new equation, which has a degree 1 less than our original equation shown below:

Leading Answer Term = x

^{(4 - 1)} = x

^{3} Since the last number in our result line = 0, we will not have a remainder and have a clean quotient which is shown below in our answer:

Answer =

3x^{3} + 21x^{2} - 18x - 216 It appears your answer forms a cubic equation since the maximum power of your result equation is 3 and your remainder is zero. Click

here to solve this cubic equation