__Using polynomial long division, evaluate the expression below:__**9x**^{3} + 4x^{2} - 6x + 1 |

**x**^{2} + 6 |

__First, we write our expression in long division format and follow the steps below.__

**Step 1** 1a) Divide the first term of the

**dividend** by the first term of the

**divisor** →

**9x**^{3} ÷

**x**^{2} = 9x

^{(3 - 2)} =

**9x** 1b) We multiply that part of the

**quotient** by the

**divisor** →

**9x**(

**x**^{2} + 6) =

**9x**^{3} + 54x →

Click here to see the Math for this Multiplication. 1c) Subtract

**9x**^{3} + 54x from

**9x**^{3} + 4x^{2} - 6x + 1 to get

**4x**^{2} - 60x + 1 →

Click here to see the Math. | | | 9x |

x^{2} | + | 6 | 9x^{3} | + | 4x^{2} | - | 6x | + | 1 |

| | | 9x^{3} | | | + | 54x | | | | | |

| | | | | 4x^{2} | - | 60x | + | 1 | | | |

**Step 2** 2a) Divide the first term of the

**dividend** by the first term of the

**divisor** →

**4x**^{2} ÷

**x**^{2} = 4x

^{(2 - 2)} =

**4** 2b) We multiply that part of the

**quotient** by the

**divisor** →

**4**(

**x**^{2} + 6) =

**4x**^{2} + 24 →

Click here to see the Math for this Multiplication. 2c) Subtract

**4x**^{2} + 24 from

**4x**^{2} - 60x + 1 to get

**-60x - 23** →

Click here to see the Math. | | | 9x | + | 4 |

x^{2} | + | 6 | 9x^{3} | + | 4x^{2} | - | 6x | + | 1 |

| | | 9x^{3} | | | + | 54x | | | | | |

| | | | | 4x^{2} | - | 60x | + | 1 | | | |

| | | | | 4x^{2} | | | + | 24 | | | |

| | | | | | | -60x | - | 23 | | | |

We have a remainder leftover. We take our answer piece and remainder piece below

Answer =

**9x + 4**Remainder piece = Leftover answer divided by our denominator