Unit 3: Exponents and Polynomials
This section introduces you to the concept of evaluating exponents, converting scientific notations to decimal notations, and vice versa. You will apply these concepts to evaluating polynomial expressions.
Completing this unit should take you approximately 19 hours.
Upon successful completion of this unit, you will be able to:
- simplify exponential expressions with positive and/or negative exponents;
- multiply or divide expressions in scientific notation;
- evaluate polynomials for values of the variable;
- add and subtract polynomials;
- distribute and multiply with polynomials (including special products); and
- divide polynomials by monomials and with long division.
3.1: Exponents
3.1.1: Rules of Exponents
Read this section. Polynomials are all about adding and multiplying powers of x. Notice that we have specific rules that govern multiplying and dividing powers of x and raising a power of x to another power.
3.1.1.1: Product Rule
Complete page 51 of Wallace's workbook to practice implementing the product rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this three-minute video, which discusses the product rule for exponents.
3.1.1.2: Quotient Rule
Complete page 52 of Wallace's workbook to practice implementing the quotient rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch these two videos, which discuss the quotient rule for exponents.
3.1.1.3: Power Rule
Complete page 53 of Wallace's workbook to practice implementing the power rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch these two videos, which discuss the power rule for exponents.
3.1.1.4: Zero Exponents
Read this section. Notice that a negative exponent in the denominator is the same as a positive exponent in the numerator. Conversely, a negative exponent in the numerator is the same as a positive exponent in the denominator.
Complete page 54 of Wallace's workbook to practice with the zero power rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this four-minute video, which discusses the zero power rule with exponents. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
3.1.1.5: Negative Exponents
Complete page 55 of Wallace's workbook to practice with negative exponents. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch these two videos, which discuss rules for negative exponents.
Watch this video, which shows a short proof of the zero exponent.
3.1.2: Properties
Complete page 56 of Wallace's workbook to solve equations using the properties of exponents. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch each of these videos, focusing on the examples used that demonstrate how to simplify exponents with the properties and rules you have learned so far, i.e., product rule, quotient rule, etc.
3.1.3: Homework Assessment
Answer the odd-numbered problems for questions 1 through 43.
Answer the odd-numbered problems for questions 1 through 39.
3.2: Scientific and Decimal Notation
Read this section. Scientific notation allows us a general idea of the size of a number with a glance at the exponent, instead of counting places before or after a decimal point.
3.2.1: Convert
Complete page 57 of Wallace's workbook to practice with converting between standard and scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this five-minute video, which demonstrates how to convert between standard and scientific notation.
3.2.2: Close to Scientific
Complete page 58 of Wallace's workbook for more practice with scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this four-minute video, paying attention to the examples being used to further explain scientific notation. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
3.2.3: Multiply/Divide
Complete page 59 of Wallace's workbook for more practice with scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this three-minute video, which discusses how to multiply and divide with scientific notation.
3.2.4: Multiply/Divide Leaving Answer in Decimal Notation
Complete page 60 of Wallace's workbook to practice with multiplying and dividing scientific notation with a result that is not in scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this four-minute video, which addresses multiplication and division and then converting the answer to scientific notation.
3.2.5: Homework Assessment
Answer the odd-numbered problems for questions 1 through 41.
3.3: Polynomials
3.3.1: Evaluate
Read this section. Evaluating a polynomial is simply plugging in a value for the variable and then simplifying.
Watch this five-minute video, which provides definitions and characteristics of polynomials and gives examples of evaluating polynomials.
3.3.2: Add/Subtract
Complete page 62 of Wallace's workbook to practice adding and subtracting polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this four-minute video, paying attention to the examples being used to add and subtract polynomials.
3.3.3: Multiply Polynomials
3.3.3.1: Monomial by Polynomial
Read this section. Multiplying polynomials is all about being careful with distribution (focus on how parentheses are used to make sure we distribute correctly) and following the rules for exponents (focus on how we use xp xq = xp+q).
Complete page 63 of Wallace's workbook to practice multiplying by monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this three-minute video, paying attention to the examples being used to explain how to multiply by monomials.
3.3.3.2: Binomial by Binomial (FOIL)
Complete page 64 of Wallace's workbook to practice multiplying by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this four-minute video, paying attention to the explain of how to multiply binomials.
3.3.3.3: Multiply with Trinomials
Complete page 65 of Wallace's workbook to practice multiplying by trinomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this five-minute video, paying attention to the explanation of how to multiply trinomials.
3.3.3.4: Multiply Monomial by Two Binomials
- Tyler Wallace's "Beginning Algebra Lab Notebook: Polynomials - Multiply Monomials and Binomials" URL
Complete page 66 of Wallace's workbook to practice multiplying monomials by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch this four-minute video, paying attention to the examples being used to explain how to multiply monomials by two binomials.
3.3.4: Special Products
3.3.4.1: Sums and Difference
Read this section. The idea of this section is to point out a few nice and important special cases of polynomial multiplication. Memorize these special products and it will pay off big later!
Complete page 67 of Wallace's workbook to practice multiplying monomials by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch these videos, paying attention to the examples used to explain sums and differences with polynomials.
3.3.4.2: Perfect Square
Complete page 68 of Wallace's workbook to practice with perfect squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch these videos, which discuss the perfect square shortcut.
3.3.5: Homework Assessment
Answer every other odd numbered problem for questions 1 through 41.
Answer every other odd numbered problem for questions 1 through 39.
Answer every other odd numbered problem for questions 1 through 39.
3.4: Division of Polynomials
3.4.1: Divide a Polynomial by Monomial
Read this section. Dividing polynomials is just the same as the long division you learned in elementary school. It is also great practice in solidifying your skills in exponents and multiplication. Pay special attention to how the exponents work as place holders just as the digits in the 1s, 10s, 100s, and so forth, places did for us in elementary school.
Complete page 69 of Wallace's workbook to practice dividing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
3.4.2: Divide a Polynomial by a Polynomial
Complete page 70 of Wallace's workbook to practice dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Complete page 71 of Wallace's workbook for more practice with dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Watch these videos, paying attention to the examples used to explain the division of polynomials. You may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.
3.4.3: Homework Assessment
Answer odd-numbered problems for questions 1 through 43. Keep in mind that you are allowed to watch the videos as often as you please to help you answer the homework problems.
Unit 3 Practice Test
Review Unit 3 before clicking on the link above to take the practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the "Unit 3 Practice Test - Answer Key".
Unit 3 Assessment
- Receive a grade
Take this assessment to see how well you understood this unit.
- This assessment does not count towards your grade. It is just for practice!
- You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.
