Topic 7 Summative Review

Adding/Subtracting Polynomials

100

Write two different fifth degree trinomials.

Answers vary

EX:

x⁵+3x-2
x²y³-7y²+2xy

200

(5x-1)+(2x-3)

7x-4

300

Sally has $4x³ in her bank account currently. She goes shopping and spend $3x on a new outfit and $2x³ on new shoes. Her friend gives her $5x³+2x²+x for her birthday. How much money does Sally have?

7x³+2x²-2x

400

Write your answer in standard form.

(2x²-4x-1)-(3x²+8x-4)

-x²-12x+3

500

What is the difference (5x²+3x-5)-(2x²+8)?

3x²+3x-13

Multiplying Polynomials - Pt 1

100

(x+7)(x-5)

x²+2x-35

200

(3x-5)(4x-9)

12x^2-47x+45

300

(4x-3y)(5x+y)

20x²-11y-3y²

400

(x+4)(x²-3x-1)

x³+x²-13x-4

500

What is the volume of a cube with a side length of 3x-1?

(3x-1)³=27x³-27x²+9x-1

Multiplying Polynomials - Pt 2

100

(b+12)(b+12)

b²+24b+144

200

-8y³(3x²y-2x+7y-1)

-24x²y⁴+16xy³-56y⁴+8y³

300

(4x-9)(4x+9)

16x²-81

400

(3a-5b)²

9a²-30ab+25b²

500

Find a value of mx²-64=(5x+8)(5x-8).

m=25

Factoring - Pt 1

100

Factor out the GCF.

-12a³-18a²+36a

-6a(2a²+3a-6)

200

Factor x²-9x+14.

(x-2)(x-7)

300

A rectangular carpet is represented by x²+18xy+45y². What could the length and width be?

x+15y, x+3y

(x+15y)(x+3y)

400

Factor 2x²+9x-5.

(2x-1)(x+5)

500

A square mirror has a 3-inch-wide frame around it. If the area of the frame alone is 96 in², what is the area of the mirror?

25in²

Factoring - Pt 2

100

What is the factored form and associated shape for a rectangular whiteboard with the expression x²+10x+25?

(x+5)², square

200

Factor 10x³+14x²-12.

2x(x+2)(5x-3)

300

Factor 9x²-49y².

(3x-7y)(3x+7y)

400

What is the radius of a cylinder that has a height of 3 in and a volume of pi(27x²+18x+3) in³? The formula for volume of a cylinder is V=pi r² h.

r=3x+1

500

The volume of a rectangular prism is 

6x³−3x²−45x.

What are expressions for the length, width, and height?

3x, x-3, 2x+5

3x(x-3)(2x+5)