Worksheet 2.3 Module 1 Worksheet
Example A.
Simplify \(\dfrac{24x^5-3x^4+12x^2}{6x^2}\text{.}\)
Expected Student Work.
Notes on the expected documentation.
You must start with the original expression to be simplified to the left of the first equal sign.
You need to use the equal sign correctly. When working with an expression, a new equal sign is placed before each new step of work and each new step of work is place on a new line.
You need to show enough work that any average student in the course would be to able follow your thought process from beginning to end, without any additional explanation from you.
The first step of work above explicitly showed the distribution step. The second step formally showed the quotient rule for exponents. If you can do those steps in your head, you do not need to write them out on paper.
DO NOT INCLUDE THIS PAGE WHEN YOU SUBMIT YOUR ASSIGNMENT
Submission Requirements.
When uploading your work to D2L's Assignment area, please make sure your scanned work is clear and legible and you include every page of your assignment. Your file needs to be uploaded using the filename structure “lastname-firstname-ws1”.
Grading Rubric.
Below is an outline of how points will be earned on each problem of this assignment. You should use this as a guide while you complete the assignment. Prior to submitting your assignment, you should check over this rubric one last time to make sure you’ve addressed all the specified items.
| Problem | Graded Aspect | Points |
| 1 a–d | Possible Points in Total | 3 |
| 2 a–b | Possible Points for Each Part | 2 |
| 3 a–e | Possible Points for Each Part | 1 |
| 4 a–b | Possible Points for Each Part | 2.5 |
| 5 | Possible Points | 3 |
General Checks.
Is your name on your assignment?
Have you used equal signs correctly?
Did you leave out the first pages of this document that say “DO NOT INCLUDE THIS PAGE WHEN YOU SUBMIT YOUR ASSIGNMENT”?
Your answer should be “Yes.” to all of these questions. If you answered “No.” to any question, you will lose some credit.
DO NOT INCLUDE THIS PAGE WHEN YOU SUBMIT YOUR ASSIGNMENT
1.
Using the polynomial \(5x^{16}y^{3}-12x^{15}+3x^{10}y^{4}-19x^{2}y^{11}-7x\text{,}\) complete the following statements.
(a)
There are terms in this polynomial.
(b)
The degree of the second term is .
(c)
The degree of the polynomial is .
(d)
The coefficient of the fourth term is .
2.
Add or subtract, as indicated. Simplify all answers.
(a)
\(\left(-5y^2+2y-4\right)+\left(-8y^2-3y+9\right)\)
(b)
\(\left(3w^4-w^2\right)-\left(4w^3-5w^2\right)\)
Simplify.
3.
\(\left(h^3\right)^5\)
4.
\(k^2\cdot k^4\)
5.
\(\left(2p^7\right)^3\)
6.
\(\dfrac{24m^9y^8}{-6m^2y^7}\)
7.
\(\left(9g^5\right)\left(g^3\right)^4-\left(14g\right)\left(g^4\right)^4\)
8.
Divide and simplify.
(a)
\(\dfrac{9t^8-18t^4+45t^3}{-9t^3}\)
(b)
\(\dfrac{-32p^{15}-20p^{35}+4p^{20}}{-4p^5}\)
9.
\(4m^7\left(3m^9\right)^2\) simplifies to \(36m^{25}\text{.}\) Explain in detail each step it takes to simplify this expression. You must have at least two separate steps explained in words, but you could have more.