Lab: Exploration of the Values of Terms in a Polynomial

Materials:

  • Computers/lap tops; 1 per student or 1 per pair of students
  • A spreadsheet program isrequired: e.g. Microsoft Excel, Numbers (Mac), or Google Spreadsheet

Getting Started:

  1. Visit the website:
  2. Click on the Lab link (on the right side of the page): “Exploration of the Values of Terms in a Polynomial Spreadsheet”
  3. Download the Excel spreadsheet file that appears. If you are using a tablet or laptop that only connects to the internet (e.g. Chrome book), save the file to your online drive (e.g. “My Drive”)
  4. Open the file with your spreadsheet program
  5. If using Excel or Numbers, the file will open
  6. If you are using Google Spreadsheet, follow the steps below:
  7. Visit Google Drive
  8. Create a new Google Spreadsheet in your drive
  9. Go to “File”  “Import”
  10. Using the “My Drive” tab, select the lab file (Excel Spreadsheet) that you saved to the drive
  11. Press the “Select” button
  12. Choose either option #2 “Insert new sheets” or option #3 “Replace spreadsheet”

Procedure:

This spreadsheet displays the values of the polynomial created by terms in row 1 as x grows from 1 to 10. The numbers in columns B, D, F, H,and J are the coefficients. The number in column L is the constant term. Answer the questions below based on the table.

  1. What is the actual polynomial represented by the values given in row 2? (Hint: from B2 to L2)
    ______
  1. What do you notice about the relative values of the terms in the original equation?
  1. Change the coefficients of each term and investigate the impact on the relative values.
    What can you conclude about the first term of the polynomial?

Lab: Exploration of the Values of Terms in a Polynomial – ANSWER KEY

Materials:

  • Computers/lap tops; 1 per student or 1 per pair of students
  • A spreadsheet program is required: e.g. Microsoft Excel, Numbers (Mac), or Google Spreadsheet

Getting Started:

  1. Visit the website:
  2. Click on the Lab link (on the right side of the page): “Exploration of the Values of Terms in a Polynomial Spreadsheet”
  3. Download the Excel spreadsheet file that appears. If you are using a tablet or laptop that only connects to the internet (e.g. Chrome book), save the file to your online drive (e.g. “My Drive”)
  4. Open the file with your spreadsheet program
  5. If using Excel or Numbers, the file will open
  6. If you are using Google Spreadsheet, follow the steps below:
  7. Visit Google Drive
  8. Create a new Google Spreadsheet in your drive
  9. Go to “File”  “Import”
  10. Using the “My Drive” tab, select the lab file (Excel Spreadsheet) that you saved to the drive
  11. Press the “Select” button
  12. Choose either option #2 “Insert new sheets” or option #3 “Replace spreadsheet”

Procedure:

This spreadsheet displays the values of the polynomial created by terms in row 1 as x grows from 1 to 10. The numbers in columns B, D, F, H,and J are the coefficients. The number in column L is the constant term. Answer the questions below based on the table.

  1. What is the actual polynomial represented by the values given in row 2? (Hint: from B2 to L2)
    _________
  1. What do you notice about the relative values of the terms in the original equation?

All of the x-values are positive, and the coefficients of the terms are almost all positive. The only exceptions are the -8 as the coefficient of the 2nd term and the constant term (which is also -8). Therefore, the end results, or outputs will all be positive numbers.

  1. Change the coefficients of each term and investigate the impact on the relative values.
    What can you conclude about the first term of the polynomial?

Answers will vary – Sample Answer:
If you change the coefficients to the lower powers, leaving the leading coefficient positive, then almost all of your outputs are positive. If you change the leading coefficient to a negative number and make the coefficients of the lower powers positive, then almost all of your outputs are negative. The reason that the patterns above occur is because the power of our 1st term is to the 5th power, and all of our x-values are positive and increasing, making the value of our 1st term extremely high (pos.) or extremely low (neg.).

Algebra II – Polynomial Functions~1~NJCTL.org