Unit 7 Polynomial Operations

Multiplying

100

Simplify: (2x²)(-11x)

-22x³

200

Simplify: (-2x)⁴

16x⁴

300

-x²(x-15)

-x³+15x²

400

(4x²)²

16x⁴

500

Simplify: -8x³(7x² - 4x - 1)

-56x⁵ + 32x⁴ + 8x³

Adding and Subtracting

100

Find the sum: 12x² + 8x²

20x²

200

(4x-5) - (9x+2)

5x-7

300

(6x²+x+7) + (3x²+1)

9x²+x+8

400

(2x²-x+3) - (5x²+3x-7)

-3x²-4x+10

500

(2x⁴-3x+9)+(-x³+12x)

2x⁴ - x³ + 9x + 9

Shapes

100

A homeowner wants to expand a square patio. The original patio is a square with side length x feet. They want to add an extension of of another square of 2 feet on all sides. What is the new side length?

x+2

200

The  garden has dimensions of length (3x+5) feet and width(2x+1) feet. What is the area?

6x²+13x+5

300

A contractor builds a rectangular building with dimensions (4x−1) meters by (3x+2) meters. What is the perimeter of the building?

14x+2

400

A company manufactures storage boxes. The base of the box has dimensions (2x) feet by (3x) feet. The height of the box is (4x) feet. Find the Volume.

24x³

500

A landscaper is designing rectangular garden beds. 

The first garden has dimensions of length (3x+5) feet and width (2x+1) feet. 

The second garden has dimensions of length (2x+3) feet and width (2x+1) feet. 

What is the area of each garden bed?

1st: 6x²+10x+5

2nd: 4x²+8x+3

Word Problems

100

A paint factory starts production with 2x+120 liters of base paint. Each production run consumes 1x+5 liters. How much will be left after one production run?

x+115

200

A pharmacy begins inventory with 5.6x²−20x+200 milligrams of a medication in stock. 

A hospital order requires 1.5x²+11x milligrams. 

How much is left after the hospital order?

4.1x²-31x+200

300

A construction supply company receives concrete deliveries from two plants. 

Plant A delivers 4.7x²−22x+110 cubic meters, and Plant B delivers 2.8x²+16x+50 cubic meters.

What polynomial represents the total cubic meters of concrete received from both plants?

7.5x²-6x+160

400

A chemical company produces materials at two production sites. 

Site A produces 5.1x²−16x+75 kilograms per batch, and Site B produces 3.2x²+10x+40 kilograms per batch.

What polynomial represents the total kilograms of material produced per batch from both sites combined?

8.3x²-6x+115

500

A hair salon operates two locations. The profit from the downtown salon is modeled by f(x)=−0.06x²+9.2x+42 dollars, and the profit from the airport salon is modeled by g(x)=−0.03x²+6.5x+31 dollars, where x represents the number of haircuts performed.

If an equal number of haircuts are performed at both locations, which polynomial function models the total profit for the salon?

-0.09x²+15.7x+73