## MTH105 Math in SocietyMath for "Real" Life

### § 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.