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Factoring
Week Two Discussion Questions
How do you factor the difference of two squares?
This expression is called a difference of two squares:
The factors of a2 - b2 are:
(a + b) and (a -- b)
How do you factor the perfect square trinomial?
Both x2 and 9 are perfect squares.
Because subtraction is occurring between these squares, this expression is the difference of two squares.
x2 = x * x
The factors are (x + 3) and (x - 3).
(x + 3) (x - 3) or (x - 3) (x + 3)
How do you factor the sum and difference of two cubes?
The sum of two cubes is factored like this:
a3 + b3 = (a + b)(a2 -- ab + b2)
The difference of two cubes is factored like this:
= (a -- b)(a2 + ab + b2)
Which of these three makes the most sense to you? Explain why.
Factoring the perfect square trinomial makes the most sense to me because the calculations seem intuitive -- nothing unexpected or complex happens. Either a square exists or it does not; factoring is a relatively simple matter for squares.
Week Three Discussion Questions
Do all rational equations have a single solution? Why is that so?
Not all rational equations have a single solution.
Given,...
It is considered "rational" because one number is divided by another number:
x2 + 5 / x + 2
This operation is just like what occurs in a ratio. But note that the polynomial that you are dividing by cannot be zero.
Week Four Discussion Questions
Write a word problem involving a quadratic function. How would you explain the steps in finding the solution to someone not in this class?
Given the area of a rectangle is 560 square inches. The length is 3 more than twice the width. Find the length and the width.
L = length
W = width.
Since the length is 3 more than twice the width, then:
L = 2W + 3
The area of the rectangle is 560, so:
LW = 560
Use L = 2W +3 to solve for W:
LW = 560
(2W = 3)W = 560
2W2 + 3W = 560 (Subtract 560 from each side of the equation)
2W2 + 3W -- 560 = 0
Use the Quadratic Formula:
W = -3+/- ? 9 --…
The increase in f (x) is most dramatic between 0 and 1. After x = 1, as x gets larger, the increasing f (x) begins to slow down -- which means the increase get smaller as x gets larger. And the f (x) are positive for x when it is greater than 1 and negative for x when it is less than 1.
Marcus, N. Graphs of exponential functions. http://www.sosmath.com/algebra/logs/log4/log42/log42.html
Purple Math http://www.purplemath.com/modules/logs.htm
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