Multiplying and Factoring Polynomials

Topics for Today:

We explored multiplying a monomial by a polynomial today and doing the reverse by factoring out the greatest common factor.  Multiplying and factoring are inverse (opposite) operations of each other.

Vocabulary: Greatest Common Factor, GCF

Sections Covered in Textbook:

9-2: Multiplying and Factoring (pages 462-465)

Resources & Tutorials:

1) How do you multiply a monomial by a polynomial?
2) How do you find the Greatest Common Factor (GCF) of monomials?
3) Factoring Monomials from Polynomials

Adding and Subtracting Polynomials

Topics for Today:

Today we began our unit on polynomials with some definitions.  We also worked on adding and subtracting polynomials.  Like working with any variable expressions, we must always look for like terms when combining their components.  Variables raised to different powers cannot be combined by adding and subtracting.  One last concept to keep in mind is that when subtracting polynomials, you must subtract each piece of the polynomial; that is, the subtraction must be distributed to each piece of the polynomial and not just its first term.

Vocabulary:  monomial, degree of a monomial, polynomial, standard form of a polynomial, degree of a polynomial, binomial, trinomial

Sections Covered in Textbook:

9-1: Adding and Subtracting Polynomials (pages 456-461)

Resources & Tutorials:

1)  What is a monomial? 
2)  What is a polynomial? 
3)  How do you find the degree of a polynomial?
4)  How do you add polynomials? 
5)  How do you subtract polynomials? 

Division Properties of Exponents

Topics for Today:

Today we tackled the last property of exponents that deals with division.

When dividing powers with the same base, we can simply subtract the exponents.  When dividing monomials, we must match up like bases with each other, and deal with them separately.

Sections Covered in Textbook:

8-5: Division Property of Exponents (pages 417-423)

Resources & Tutorials:

1) What's the quotients of powers rule?
2) How do you divide monomials using the quotients of powers rule?
     (*This video leaves a negative exponent - that is NOT simplest form!*)

More Multiplication Properties of Exponents

Topics for Today:

Today we reviewed the topics relating to exponents and exponent rules, including scientific notation.  We expanded our topic of multiplication of powers to include raising a power to a power, as well as taking a monomial to a power.  When a monomial (a number, a variable, or a product of a number and variable - this also includes whole number exponents) is raised to a power, each element of that product must be raised to that power.

Sections Covered in Textbook:

8-4: More Multiplication Properties of Exponents (pages 411 - 415)

Resources & Tutorials:

1) What the power of a power rule?
2) How do you take a monomial to a power?
3) More on the power of a product rule.

Multiplication Properties of Exponents

Topics for Today:

Today we discussed how to manage multiplying powers with the same base.  We looked at several examples as well as explored how to multiply numbers together that are in scientific notation.  In summary, when multiplying powers with the same base, just keep the base and add the exponents together.  This process works for both positive and negative exponents.

Graphic Credit: https://www.onlinemath4all.com/multiply-powers.html

Sections Covered in Textbook:

8-3: Multiplication Properties of Exponents (pages 405-410)

Resources & Tutorials:

1) What is the product of powers rule? 
2) How do you find the product of powers? 
3) How do you multiply numbers using scientific notation? 

Scientific Notation

Topics for Today:

Today we used exponents in a practical way when we learned about scientific notation.  Scientific notation is simply a way to write very large and very small numbers that follow a few rules.

Simply stated, scientific notation is the product of a number and a power of 10 that follows the format: 

a x 10ⁿ  where n is an integer and 1 ≤ a < 10

Image credit: https://pt.slideshare.net/jessicagarcia62/compute-with-scientific-notation/6?smtNoRedir=1

Vocabulary:  scientific notation

Sections Covered in Textbook:

8-2: Scientific Notation (pages 400-404)

Resources & Tutorials:

1) What's scientific notation? 
2)  How do you convert decimal notation to scientific notation? 
3) How do you convert from scientific notation to decimal notation? 
4) How do you order numbers in scientific notation? 

Zero and Negative Exponents

Topics for Today:

We began a discussion about powers, bases and exponents today, and focused on bases with a zero exponent as well as negative exponents.

Summary

• Any non-zero number raised to the zero power equals one!
• Negative exponents are fractions.  If a factor is moved up or down in a fraction, the sign of the exponent is changed.  

Sections Covered in Textbook:

8-1: Zero and Negative Exponents (pages 394-399)

Resources & Tutorials:

1) What do you do with a zero exponent? 
2) What do you do with a negative exponent?