Factoring Week Two Discussion Questions How Do

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, for example: f (x) = (x2 + 2x + 1)/(x^4 + 2) Then, x can be any real value, which will result in many possible solutions. What constitutes a rational expression? How would you explain this concept to someone unfamiliar with it? A rational express is the ratio of two polynomials.

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 -- 4 (2) (-560) / 2.2 = W = -3+/- ?4489 / 4 = -3+/- 67 / 4 = -70 / 4 Or 64 / 4 = 16 But since the width can't be negative, then: L = 2 * 16 + 3 = 35 What is the relationship between exponents and logarithms? How would you distinguish between the two, using both a graph.