Lesson 5: Operations on Polynomials

Poll

On a scale of 1-5, how confident do you feel about performing addition and subtraction on polynomials?

Ex) $$\left(2x^2+3x+1\right)+\left(x^2+4x+5\right)$$  

• 1. I do not remember anything about polynomials

• 2. I need to review the vocabulary and how to perform each operation

• 3. I remember some of the operations, but I could use some more help

• 4. I am comfortable with addition and subtraction and feel fairly confident

• 5. I am ready to move on to multiplication and division

Important vocabulary

​Monomials

Important vocabulary

​Monomials

​Binomials

Important vocabulary

​Monomials

​Binomials

​Trinomials

​Polynomials

Important vocabulary

Terms

• ​Another name for monomials

Important vocabulary

Terms

• ​Another name for monomials

​Like Terms

Important vocabulary

Terms

• ​Another name for monomials

​Like Terms

​Degree

Important vocabulary

Terms

• ​Another name for monomials

​Like Terms

​Degree

​Degree of a polynomial

• The largest degree out of ALL terms

Important vocabulary

Terms

• ​Another name for monomials

​Like Terms

​Degree

​Degree of a polynomial

• The largest degree out of ALL terms

Leading Coefficient

• The coefficient of the term with the largest degree

Distributive Property

Distributive Property

Distributive Property

Fill in the Blank

Try performing the following operation on the polynomial:

$$\left(2x^2+3x\right)-4\left(x^2-4\right)$$  

Adding/Subtracting Polynomials

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Multiplying Polynomials

​When multiplying polynomials, we use the DISTRIBUTIVE property

Multiplying Polynomials

​When multiplying polynomials, we use the DISTRIBUTIVE property

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Lesson 5.pdf - Google Drive

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Lesson 5.pdf - Google Drive

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Fill in the Blank

Multiply the following: $$\left(x+2\right)\left(x-2\right)\left(x+1\right)$$  

Dividing Polynomials

​We can do the same for dividing polynomials by monomials!

Fill in the Blank

Divide the following Polynomials: $$\frac{-2x^4+4x^5}{2x^3}$$  

Dividing Polynomials

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Dividing Polynomials

Lesson 5.pdf - Google Drive

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Dividing Polynomials

Lesson 5.pdf - Google Drive

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Poll

How confident do you feel about the material you learned today?

• 1

• 2

• 3

• 4

• 5

​Reminders:

• There are exam resources in Lon Capa

• Practice Problems for Exam 1, Timed Practice Exam, and Difficult problems from past exams

• The difficulty of the exam is very similar to the above resources!

• Come to supplemental instruction, use COSINE, Math Resource Room, Piazza, etc.

​Reminders:

• SIGN UP FOR EXAM IN LON CAPA

• No Class on Monday

• Homework due on Sunday

• Exam #1 is Next Thursday

• Wednesday's Class will review material for the first exam

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