Factor the polynomial. Steps: GCF(leftovers) then reverse FOIL the leftovers

4x³ – 36x² + 72x

Version A Name: ____________Hour: __________

Practice Makes Perfect- Operations with Polynomials

Directions: There are three sections to this assignment. Section I focuses on adding and subtracting polynomials. Section II focuses on multiplying polynomials. Section III focuses on factoring polynomials.

Please show your work for each problem.

SECTION I: Adding and Subtracting Polynomials.

1. Add the following polynomials using either the vertical or horizontal method.

(11x³ + x² - 8x) + (2x³ - 7x + 4)

2. Subtract the following polynomials using either the vertical or horizontal method.

(10x³ - 3x² + 7) – (-12x³ - 6x² + 5x + 5)

SECTION II: Multiplying Polynomials.

3. Multiply.

( 2x² - 3x + 4 )( 5x – 6 )

4. Multiply.

7x⁵(4x³)(-2x)

5. Multiply.

( 3x - 3 )( x – 6 )

6. Multiply.

2x³y( x² – 6y )

SECTION III: Factoring Polynomials

7. Find the GCF (Greatest Common Factor) of the following monomials.

8x³ and 20x and 56x⁴

8. Factor the polynomial using GCF(leftovers).

-15x³ - 6x² - 12x⁴

9 Factor the trinomial using reverse FOIL.

x² – 5x - 36 = ( )( )

10. Factor the trinomial using reverse FOIL.

-2x² + 4x + 12 = ( )( )

11. Without using reverse FOIL, use the special binomial products to factor the following:

4x² + 20x + 25 = ( )( ) x² – 6xy + 9y² = ( )( ) 16x² – 49 = ( )( )

12. Factor the polynomial using multiple methods.

4x³ – 36x² + 72x

Appendix F:

Functions Unit

Includes:

Formative Assessment (Real World Connections & Conceptual Understanding) Lesson Plan- Functions (Conceptual Understanding)

Choice Activity- Functions (Differentiation)

Independent and Dependent Variables Activity (Real World Connections) Formative Assessment: Continuous vs. Discrete (Conceptual Understanding)

Performance Assessment (Real World Connections)

Cubic Functions Activity (Differentiation & Conceptual Understanding) Unknown Functions Activity (Active Learning)

Exponential Functions Activity (Differentiation)

Name_______________

Period_______________

Date_______________

FUNCTIONS: Money and Cell Phones

Objective:

Throughout this unit we have been learning all about functions. Over the past several days, we have worked on writing and evaluating functions. This assessment will help us see whether you have mastered these two learning objectives. It is important to know if you need more practice on these targets because you must be able to write and evaluate functions before you can graph functions. You guessed it…graphing functions is where we are heading next in this unit. 

Directions:

♦ Please put your name, class period, and the date in the upper right hand corner of each test page.

♦ There are two questions on this assessment. Each question has its own set of directions and its own scoring rubric. Make sure that you read the directions for each question carefully. Check out each scoring rubric before answering the question so you know what I expect in your answer. The scoring rubrics are located at the end of the assessment.

♦ Please write your answers in the space provided to you after each question. If you need more room for your answer, you may use a separate piece of paper and staple it to the assessment.

♦ You will have until the end of this class period (approximately twenty

minutes) to complete this assessment. If you need more time, please see me to set up a time for you to come in and finish.

♦ If you have a question, please raise your hand and I will come to you at your seat.

♦ When you are finished, please place this assessment in the turn in tray for your class period. Then quietly return to your seat and work on your tic-tac-toe board for this unit.

Please take your time and do your best work. I am excited to see the excellent answers and great explanations you come up with! 

Name_______________

Period_______________

Date_______________

Question 1: Prompt

In this unit we have become familiar with functions and the ways they can be displayed. While it is true that functions are usually written as equations,

sometimes functions are written as word problems or shown as raw data. For this question, you will be analyzing a data table in order to write a function (in equation form) for the data. You must write the correct equation in function notation and provide a detailed explanation of how you used the data to figure out your answer. You must also describe the relationship between Zeke’s pay and the function equation by identifying what each number and variable represent. Looking for a relationship between Zeke’s hours and his earnings might be a good place to start.

Function for Zeke’s Pay: _____________________

How did you figure out your answer? What part of Zeke’s pay does each variable and number represent?

Zeke’s Pay Over Six Weeks Week Hours Worked $ Earned

Name_______________

Period_______________

Date_______________

Question 2: Scenario

We recently learned how to evaluate functions by plugging in input values and solving. You will find that this knowledge can be extremely useful in everyday situations. Imagine your friend just got a cell phone (woo-hoo!) and needs your help deciding which calling plan to sign up for. He is looking for a plan that lets him talk to you and his other friends each month for a low price. There are two plans that he can get with his phone. The first plan costs ten dollars a month plus ten cents per minute that you talk. The second plan costs twelve cents per minute without an additional monthly charge. These two plans are written in function notation in the tables below. Evaluate the function for each plan using input values of 0, 225, 500, 850, and 1,000 minutes. Then analyze the data and decide which calling plan your friend should get if he will talk 500 minutes or less per month. In the space provided, tell which plan your friend should choose and explain why. Make sure to use data to support your decision.

Calling Plan # 2 Function: f(x) = .12x

Number of Minutes Total Cost 0

225 500 850 1,000

Which calling plan should your friend choose? _____________

Explain why.