Introduction to Polynomials

​Quarter 2 - Week 8

​WELCOME TO MATH 7

​LEARNING OBJECTIVES

​1

​2

​3

​classify algebraic expressions which are polynomials according to degree and number of terms;

​identify and differentiate the types of polynomials; and

​distinguish right and wrong.

Algebraic Expression (Number of Terms)​

​DRILL ACTIVITY

Fill in the Blanks

Identify the number of terms in :

$8x^2-5x+6$  

Fill in the Blanks

Identify the number of terms in :

$5n$   

Fill in the Blanks

Identify the number of terms in :

   $3a^3+6$  

Fill in the Blanks

Identify the number of terms in :

   $v^2+c^3+8-5b^5$   

Fill in the Blanks

Identify the number of terms in :

   $6$    

Answer the following questions about the parts of an algebraic expression​.

​Coefficient, Variable, Constant

​REVIEW

Multiple Choice

In the expression below, which is the constant?

$$10-y$$  

• -y

• 1

• 10

• There are no constants in the expression.

Multiple Choice

Identify the variable in the expression.

$$2b^2-4b+6$$  

• 2b

• b

• 6

• a

Multiple Choice

What are the coefficients in the expression $$6c^2-5b-3?$$  

• 6, -5, and -3

• 6 and 5

• 6 and -5

• 6, 5, and 3

Multiple Choice

In the expression below 2 and 3 are the ___

$$2x+3y-4$$  

• Variables

• Constants

• Terms

• Coefficients

Multiple Choice

Which algebraic expression has 3 terms?

• 2x - 3w + 10

• 14b - 2

• 4y

• 5m + 2g - 4y - 6

​INTRODUCTION TO POLYNOMIALS

Identify and differentiate the types of polynomials.

​POLYNOMIAL

​The definition of a polynomial as algebraic expressions containing exponents that are non-negative integers means that zero can be an exponent of a variable. Any constant is considered a polynomial.

Multiple Choice

Is the given POLYNOMIAL or NOT?

$$10x^{-1}+6x^2$$  

• Polynomial

• Not a Polynomial

Multiple Choice

Is the given POLYNOMIAL or NOT?

$$x^3+6c\ -\ 9$$   

• Polynomial

• Not a Polynomial

Multiple Choice

Is the given POLYNOMIAL or NOT?

$$\sqrt[]{x}-2$$    

• Polynomial

• Not a Polynomial

Multiple Choice

Is the given POLYNOMIAL or NOT?

$$\frac{3+x}{x}$$     

• Polynomial

• Not a Polynomial

Multiple Choice

Is the given POLYNOMIAL or NOT?

     $$y^{\frac{1}{2}}+3y-8$$  

• Polynomial

• Not a Polynomial

​NOT POLYNOMIAL

1. A variable has a negative exponent.

2. A variable cannot be inside a radi​cal sign.

3. ​A variable cannot be a denominator.

4. ​A variable cannot be an exponent.

5. ​The exponent is a fraction or decimals.

​Classification of Polynomials

​Polynomials are classified according to the number of terms.

Open Ended

What can you say about the number of terms of the polynomial below?

$$3n$$

  $$5x^2$$  

$$12d^2e^4f$$  

Open Ended

What can you say about the number of terms of the polynomial below?

$$3n+6$$

  $$5x^2-x$$  

$$12d^2e^4f-15e^5$$  

Open Ended

What can you say about the number of terms of the polynomial below?

$$3n+9n^2-6$$

  $$5x^2-x+24$$  

$$12d^2e^4f-e^4+48f^2$$  

​A polynomial with 1 term.

Examples: ​

3n​, 5x², 6abc⁵

​​MONOMIAL

​A polynomial with 2 terms.

Examples: ​

3n+2​, 5x²-x, 6abc⁵+4a​

​​BINOMIAL

​A polynomial with 3 terms.

Examples: ​

3n+2d-6​, 5x²-x-25​

​​TRINOMIAL

​CLASSIFICATION OF POLYNOMIALS

​

​

​

​Standard Form

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.

Multiple Choice

Which polynomial is written in standard form?

• -11 - 3x + 8x² + 9x³

• 8x² + 9x³ -11 - 3x

• 9x³ + 8x² - 3x - 11

• 12 - 10x - 3x³ - x²

Multiple Choice

Put in Standard Form. 12 - 3x³ - 10x - x²

•  - 3x³ - x² - 10x + 12

•  3x³ - x² + 10x + 12

• 12 - 3x³ - 10x - x² It is in Standard Form.

• 12 - 10x - 3x³ - x²

​Degree of a Polynomial

The degree of a polynomial ​is equal to the largest exponent of any term of the polynomial.

​

Note: You have to ensure that the expression is in standard form.​

​Degree of a Polynomial

EXAMPLE:​​

​Degree of a Polynomial

EXAMPLE:​​

​Degree of a Polynomial

EXAMPLE:​​

​Second degree

Multiple Choice

Classify the degree:

9x⁴

• 1st degree

• 2nd degree

• 3rd degree

• 4th degree

Multiple Choice

Classify the degree:

$$4s^4-12st+6s^3t^4$$  

• 1st degree

• 4th degree

• 7th degree

• 12th degree

Multiple Choice

What is the leading term?

$$4s^4-12st+6s^3t^4$$  

• $$4s^4$$  

• $$-12st$$  

• $$12st$$  

• $$6s^3t^4$$  

Multiple Choice

What is the leading coefficient?

$$4s^4-12st+6s^3t^4$$  

•  6

• - 12

• 4

•  7

Fill in the Blanks

What is the degree of this polynomial?

2x⁴ - 3x⁵ + x

(1st, 2nd, 3rd,...)

Multiple Choice

What is the leading term?

$$2x^4-3x^5+x$$  

• $$4s^4$$  

• $$-12st$$  

• $$12st$$  

• $$6s^3t^4$$  

Multiple Choice

What is the leading coefficient?

$$2x^4-3x^5+x$$  

•  3

• - 3

• 2

•  -2

​REMINDERS:

​1.) Lesson Discussed: Polynomials

2.) Asynchronous Task: Written Work about Evaluating Algebraic Expression​

3.) Review for the 2nd QA next meeting.​