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?

ยง 3.2 Polynomial Factors, Zeros, and Remainders

Is x-2 a factor of x3-3x2+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 

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.

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