Topic 3-1 & 3-2 Jeopardy!

Key Features of Polynomial Functions

100

What is the degree and leading coefficient of the following polynomial function?

2x⁸ - 14x³ + 22 - x⁹

Degree: 9

Leading Coefficient: -1

200

What is the degree and leading coefficient of the following function?

x² - 12x + 14 - 3x³ + x³ - 7x²

Degree: 3

Leading Coefficient: -2

300

Rewrite the function in standard form and state its degree and leading coefficient:

17x - 19 + 2x + 8 + 4x²

Standard Form: 4x² + 19x -11

Degree: 2

Leading Coefficient: 4

400

Rewrite the function in standard form and state its degree and leading coefficient:

3x³ + 4 - 12x³ + x⁶ - 12 + x² - 4x⁶

Standard Form: -3x⁶ - 9x³ + x² - 8

Degree: 6

Leading Coefficient: -3

500

Rewrite the function in standard form and state its degree and leading coefficient:

6x¹⁰ - 17x + 2x² + x¹⁰ - 5x⁷ + 18 - 6x + 5

Standard Form: 7x¹⁰ - 5x⁷ + 2x² - 23x + 23

Degree: 10

Leading Coefficient: 7

Graphs of Polynomial Functions

100

What is the maximum number of turning points this function can have:

8x⁷ - 14x + 56

6

200

What is the maximum number of turning points this function can have:

3x - 26x² + x⁴ - 17x⁵ + 39

4

300

What is the end behavior of the following function: 

-2x¹⁸ - 7x³ - 22

As x-->infinity, y-->negative infinity

As x-->negative infinity, y-->negative infinity

400

What is the end behavior of the following function:

6x - 2x³ + 18 - 2x²

As x-->infinity, y-->negative infinity

As x-->negative infinity, y-->infinity

500

What is the end behavior of the following function:

5x⁸ + 2x⁸ + 16x⁴ - 12x⁷ - x⁸ + 3 - 4x + 19

As x-->infinity, y-->infinity

As x-->negative infinity, y-->infinity

Adding and Subtracting Polynomial Functions

100

Add (4x³−2x²+4x+15) + (x⁴−8x³−9x−6)

x⁴ - 4x³ -2x² - 5x + 9

200

Subtract (6x⁴ - 4x³ + 2x² + 9) - (x⁴ + 3x² - 1)

5x⁴ - 4x³ - x² + 10

300

Subtract (6xy - 2x + y + 4) - (12xy + 14x - 10y)

-6xy - 16x + 11y + 4

400

Add (y⁴ + 3x²y² - 8xy + 9) + (6y⁴ - 9x²y² + 14)

7y⁴ - 6x²y² - 8xy + 23

500

Subtract (4m³n + 3mn - 18) - (9m³n - 10m²n² - 2)

-5m³n + 10m²n² + 3mn - 16

Multiplying Polynomial Functions

100

Multiply (2x+5)(2x-11)

4x² - 12x -55

200

Multiply (4y² - 2)(6y + 1)

24y³ + 4y² - 12y - 2

300

Multiply (4b - 8)(2b² - 3b + 1)

8b³ - 28b² + 28b - 8

400

Multiply 5xy(3x² - xy + 2y²)

15x³y - 5x²y² + 10xy³

500

Multiply (c²d + 3cd)(2cd² - 6cd + 5)

2c³d³ - 6c³d² + 5c²d + 6c²d³ - 18c²d² + 15cd