## [SOLVED] Factoring Polynomials and Rational Expression Essay Questions!

Hi everybody, I will have an odd dilemma facing me tomorrow morning at 8! I have my last College Algebra test before finals and this one will involve 3 short answer/essay questions. My teacher gave me the sample essays she had used in the past (and will select the 3 from) and I honestly have no idea how to prepare for all the possibilities! I hope someone here would find the time to help me answer these. Here are the ones relevant to this test:

1.Fully develop the concept of a polynomial as it relates to the following:
·The definition – Give examples of polynomials and functions that are not (and why). A more formal definition will receive more credit.
·Classification – Be sure to explain full classification with examples.
·Proper way to write (or present) a polynomial – Why is this the “proper” way?

2. Compare and contrast the various methods and approaches for factoring binomials, trinomials, and polynomials with 4 terms. Makes sure to fully explain the different methods, including any techniques and formulas used. Provide examples to aid in your discussion. To save time, you may refer to problems on this test for illustrative purposes.

3.State, and then explain, the zero-factor property. Discuss how the property has been utilized in this course, including an example. In doing so, clearly show how the property applies.

4.State and then explain the remainder theorem. Provide examples of how the theorem applies.

5.Consider the polynomials P(x) and G(x). Discuss the significance of the value of the remainder when P(x) is divided by G(x). What conclusions can be drawn simply by knowing the value of the remainder? Include relevant examples.

6.Compare and contrast how the concept of the least common denominator is “used” when adding/subtracting rational expressions as opposed to solving rational equations. You must include at least one example of each to aid in your discussion.

7.Define a rational expression and explain how to find the domain of such an expression. Provide several examples.

8.Discuss the four main criterion used to determine if a radical expression (written in radical notation) is simplified. State each criterion separately. For each case give an example of a radical expression failing to meet the criteria, then clearly show the process used to rectify the situation so that the expression is then properly simplified.

9. Develop the concept of an extraneous solution. What is an extraneous solution? In general how are they introduced into an equation? During your discussion compare and contrast how we dealt with extraneous solutions in rational equations as opposed to radical equations.