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.