Topic1: Polynomials

Topic 1: Polynomials

Classifying Polynomials 

Terms and Coefficients

Degree of a Polynomials & Constants

Standard Form of a Polynomial

Multiple Choice

What is a polynomial?

• one or more terms (separated by addition or subtraction) whose variables have whole number exponents

• one or more terms (separated by multiplication or division) whose variables have whole number exponents

• one or more terms (separated by addition or subtraction) whose variables have integer number exponents

• one or more terms (separated by multiplication or division) whose variables have integer number exponents

Fill in the Blank

In the example

$$5v^3-7$$  the constant is:

-

Fill in the Blank

How many terms are in the polynomial

$$3x^2+4x-8$$  

Fill in the Blank

What are the coefficients of the polynomial

$$-4n^5+6n^4-7$$  , separate them with a comma

Fill in the Blank

What is the degree of the polynomial

$$3x^8y+7xy^2-5x^5y^4$$  

Multiple Choice

Which of the following is a trinomial

• $$5x^2+12$$

• $$3a^2b+8$$

• $$9pqr$$

• $$5x^2-3x+17$$

Multiple Select

Which of the following polynomials are in "standard form" or the correct order.

(Choose three)

• $$3x^8+2x^5-9$$

• $$10+8p^2-6p$$

• $$4a^2-14$$

• $$5y^8+5x^7+5x^6$$

• $$144-x^2$$

Fill in the Blank

What is the degree of the polynomial

$$3x^8y+7xy^2-5x^5y^4$$  

Multiple Choice

Which of the following is a 5th degree trinomial with a leading coefficient of -2? 

• -2x⁵ + 3x - 1
• 5x^-2 +3x - 1
• -2x⁵ + 3x⁴ + 2x³ + x² - 10
• 2x + 5

Multiple Choice

What is the leading coefficient in the polynomial 3x²-2x+5?

• 3
• 2
• 5
• 0

Multiple Choice

What is the leading coefficient? 
f(x)=5x²+3x³-2x+1

• 5
• 3
• -2
• 1

Multiple Choice

Classify by the DEGREE:
2x² - 5

• Degree of 1
• Degree of 2
• Degree of 3
• Degree of 4

​Like Terms: share the same variable with the same exponents.

​Example 1:

​Example 2:

Multiple Choice

Combine like terms to simplify:

(5x + 2) + (4x - 5)

• 9x -3

• -9x-7

• 9x+7

• x+7

Multiple Choice

Simplify the expression.
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

• 11a³ - 4a² - 14a - 7 
• 5a³ - 4a² - 14a - 7 
• 5a³ - 4a² - 20a - 7 
• 5a³ - 9a² - 20a - 7

Multiple Choice

Add or Subtract to Simplify:

(4x²+ x) - (x²+ 2x)

• 3x² - x

• 4x² + 2x

• 3x² + 3x

• 3x² + 2x

Multiple Choice

Add or Subtract to Simplify:

(5x + x² - 4) - (4x - x² + 6)

• 2x² + x + 2

• x + 2

• 2x² + x - 10

• x - 10

Multiple Choice

Simplify each expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3 
• -7n² - 8n + 3 
• -6n² - 8n + 3
• -7n² - 4n + 3

Multiple Choice

(x³-x²+4) - (3x³-2x²+3)

• -2x³-3x²+7

• -2x³+x²+1

• 2x³-3x³-1

• 4x³-3x²+7

Multiplying Bionomials

TAKE NOTES: Please get paper for next problems

Learning Intention: We will learn how to multiply binomials

Learning Criteria: We can use the Box method to multiply:
(x +3) (x +4)

Multiple Choice

Write the expanded (general) form of the product (x+3)(x+6).

• x²+18x+9

• x²+9x+18

• x²+18x+18

Multiple Choice

Find the product:
(y - 3)(y + 7)

• y² - 21
• y² + 10x - 21
• y² + 4y - 21
• 2y - 10

Multiple Choice

Simplify
(p − 8)²

 Hint: (p − 8)² = (p − 8)(p − 8)

• p ² − 16p − 64 
• p ² + 16p + 64 
• p ² − 16p − 8
• p ² − 16p + 64 

Multiple Choice

Expand and simplify:

(x + 5)²

• x² + 25

• x² + 10x + 25

• x² + 10 x + 10

• x² + 10

Multiple Choice

 
What is the product of (r + 7) and (r − 7) ?

• r ² − 49 
• r ² + 14
• r ² − 7r + 49 

Multiple Choice

The length of a rectangle is x + 2 units and the width is 3x + 7

units. Find the area.

(Hint: area = length x width)

• 3x² + 9x + 14 square units

• 3x² + 13x + 14 square units

• 4x + 9 square units

• 8x + 18 square units

Multiple Choice

Find the product of :
(3x – 1)(x + 5) 

• 3x² + 4x + 5
• 3x² + 4x - 5
• 3x² + 14x + 5
• 3x² + 14x - 5

Multiple Choice

What is the product of (3p - 3) and (p - 1) when written in standard form?

• 3p² + 6p + 3

• 3p² - 6p + 3

• 3p² - 6p - 3

• 3p² + 6p - 3

Multiple Choice

What is the product of (2x + 3) and (2x - 3) when written in standard form?

• 4x² - 9 
• 4x² + 9
• 4x²- 12x - 9
• 4x² + 12x - 9

Poll

What do you need more help with?

(You can choose more than one)

• I mastered it all!

• Classifying Polynomials (terms, degree, leading coefficient, standard form)

• Adding and subtracting Polynomials

• Multiplying Binomials