## Calculus Path

## Statistics Path

## MTH111

College Algebra

PreCalculus, part 1

## vs.

## MTH105

Math in Society

Math for "Real" Life

#### Which class is right for you?

Is calculus in your future or NOT?

### § 3.2 Polynomial Factors, Zeros, and Remainders

Is `x-2` a factor of `x^3-3x^2+4x-5`

One way to check is with long division to find the quotient and remainder. If the remainder is zero then `x-2` is a factor.

`x-2 \ bar(")"\ x^3-3x^2+4x-5)`

What do you multiply by `x` to get `x^3`?

Guess: `x^2` and multiply:

`x^2` | ||||

`x-2` | `)x^3` | `-3x^2` | `+4x` | `-5` |

`x^3` | `-2x^2` |

Now subtract:

`x^2` | |||||

`x-2` | `)` | `x^3` | `-3x^2` | `+4x` | `-5` |

`-(x^3` | `-2x^2)` | ||||

`-1x^2` | `+4x` |

What would you multiply by `x` to get `-1x^2`?

Guess: `-1x` and multiply.

`x^2` | `-1x` | ||||

`x-2` | `)` | `x^3` | `-3x^2` | `+4x` | `-5` |

`-(x^3` | `-2x^2)` | ||||

`-1x^2` | `+4x` | ||||

`-1x^2` | `+2x` |

Now subtract:

`x^2` | `-1x` | ||||

`x-2` | `)` | `x^3` | `-3x^2` | `+4x` | `-5` |

`-(x^3` | `-2x^2)` | ||||

`-1x^2` | `+4x` | ||||

`-(` | `-1x^2` | `+2x)` | |||

`2x` | `-5` |

What would you multiply by `x` to get `2x`?

Guess: `2` and multiply.

`x^2` | `-1x` | `+2` | |||

`x-2` | `)` | `x^3` | `-3x^2` | `+4x` | `-5` |

`-(x^3` | `-2x^2)` | ||||

`-1x^2` | `+4x` | ||||

`-(` | `-1x^2` | `+2x)` | |||

`2x` | `-5` | ||||

`2x` | `-4` |

Now subtract.

`x^2` | `-1x` | `+2` | |||

`x-2` | `)` | `x^3` | `-3x^2` | `+4x` | `-5` |

`-(x^3` | `-2x^2)` | ||||

`-1x^2` | `+4x` | ||||

`-(` | `-1x^2` | `+2x)` | |||

`2x` | `-5` | ||||

`-(` | `2x` | `-4)` | |||

`-1` |

Solution: Since the remainder is `-1` and not `0` then `x-2` is not a factor of `x^3-3x^2+4x-5`

CHECK:

If `x-2` is a factor then `f(2)=0`
`f(2)=(2)^3-3(2)^2+4(2)-5=-1` Not `0`.

### Chapter 4: Finance

Problem Situation: Find the monthly payment for a home mortgage of $148,500 at 4% for 30 years.

Here is a spreadsheet for this loan.

Details:

House = | $165,000.00 |

10% down = | $16,500.00 |

Loan = | $148,500.00 |

APR = | 4% |

Years = N = | 30 |

k = | 12 |

Payment = | $708.96 |

Total Payments = | $255,226.22 |

Total Interest = | $106,726.22 |

The first few months:

months | Payment | Interest Due | Balance Reduction | Balance |

0 | $148,500.00 | |||

1 | $708.96 | $495.00 | $213.96 | $148,286.04 |

2 | $708.96 | $494.29 | $214.67 | $148,071.36 |

3 | $708.96 | $493.57 | $215.39 | $147,855.97 |

4 | $708.96 | $492.85 | $216.11 | $147,639.86 |

5 | $708.96 | $492.13 | $216.83 | $147,423.04 |

6 | $708.96 | $491.41 | $217.55 | $147,205.48 |

##### Disclaimer:

You should check with your advisor before taking a math class leading to calculus. Algebra classes are known to cause stress, anger, depression, and occasionally rashes, as well as lead to calculus. Please consult a physician if negative symptoms persist.