Operations with Polynomials

Adding Polynomials

100

(6x²-4x+2) + (2x²+x-4)

8x²-3x-2

200

(-7x² + 3) + (-x²)

-8x² +3

300

(5x² -2x + 3) + (x² +x +2)

6x² - x + 5

400

(x² - x - 1) + (6x - 3)

x² + 5x - 4

500

(3a²b - 6ab² + 2a) + (4ab² - 3b - 2a²b)

a²b-2ab² + 2a - 3b

Subtract Polynomials

100

(5x² - 2x + 1) - (6x² + x -3)

-x² -3x + 4

200

(6x³ + 3x² -2x - 7) - (8x³ -2x² -4x + 5)

-2x³ + 5x²  + 2x -12

300

(2x³y - 6y + 7x³) - (-3x³y + 6y + 2x³)

5x³y + 5x³

400

(3x² - 6x + 2) - (8x + 6 - 5x²)

8x² - 14x - 8

500

(4m³ - m²n + 6m³) - (5m²n - m³ + 7mn²)

11m³ - 6m²n - 7mn²

Multiplying Polynomials

100

5(2x³+3x +1)

10x³ + 15x + 5

200

12x⁵(5x⁴)

60x⁹

300

6a⁴b(4a³b²)

24a⁷b³

400

5x(2x² + 7) - 3x³ + 4

7x³ + 35x + 4

500

What is the product of 4x and 5x² + 3x + 1?

20x³ +12x² + 4x

Word Problems

100

The profit from a company's factory in North Dakota is given by n² - 15n + 23.  The company's profit from their factory in Florida is given by n² -20n -14.  Write a polynomial that represents the total profit of the two plants.

2n² -35n +9

200

The volume of a rectangular prism, in cubic inches, is given by the expression 5x³ - 6x² - 7x -14.  The volume of a larger rectangular prism is given by the expression x³ + 3x² - 5x + 7.  What is the difference between the volume of the larger prism and the smaller prism?

-4x³ + 9x² + 2x + 21

300

David is building a new garden in his yard.  The length of the garden is represented by the polynomial 3x² + 2x -4.  The width of the garden is represented by the polynomial 2x.  Write a polynomial that represents the perimeter of the garden.

6x² + 8x - 8 

400

DAILY DOUBLE

What operations are polynomials closed under?

Addition, Subtraction, and Multiplication

500

David is building a new garden in his yard.  The length of the garden is represented by the polynomial 3x² + 2x -4.  The width of the garden is represented by the polynomial 2x.  Write a polynomial that represents the area of the garden.

6x³ + 4x² -8x