Polynomials

Adding/Subtracting

100

(3x²+9x-4)+(x²+2x-2)

4x²+11x-6

200

(-3x²-2x-6)-(2x²+3x-2)

-5x²-5x-4

300

(5x²+2x-3)-(2x²+4x-3)

3x²-2x

400

(5x³+2x+4)+(3x²+9)

5x³+3x²+2x+13

500

(8x⁵-2x⁴-3x²+2)-(-3x⁴-3x²-19)

8x⁵+x⁴+21

Multiplying/GCF

100

(x+3)(x-8)

x²-5x-24

200

Find the GCF

12x⁵+8x³+2x²

2x²

300

(4x-3)(2x+3)

8x²+6x-9

400

Find and factor out the GCF

18x⁶y³+12x²y⁴-24x⁸y³

6x²y³(3x⁴+2y-4x⁶)

500

5x⁴y³(3x²y+2xy²+3)

153x⁶y⁴+10x⁵y⁵+15x⁴y

Factoring

100

x²+12x+20

(x+2)(x+10)

200

x²+2x-80

(x-8)(x+10)

300

3x²+10x-8

(3x-2)(x+4)

400

5x²-43x-18

(5x+2)(x-9)

500

12x²+10x+2

2(3x+1)(2x+1)

Solving

100

(x+2)(x-8)=0

x=-2 or x=8

200

x²-x-6=0

x=3 or x=-2

300

8x²+22x+15=0

x=-3/2 or x=-5/4

400

10x²-3x-1=0

x=-1/5 or x=1/2

500

4x²-49=0

x=-7/2 or x=7/2

Word Problems

100

Digital images are composed of thousands of pixels rendered as squares. Suppose the area of a pixel is 4x²+20x+25. What is the length of one side of the pixel?

2x+5

200

If one factor of 7x² y²+5xy² is xy², then what is

    the other factor?

7x+5

300

The perimeter of a triangle is 7x²+15x-8. If one side is 2x – 1, a second side is 7x + 7x², what is the length of the third side?

6x-7

400

The area of a rectangle is 6x²-x-2  What are the possible dimensions of the rectangle? Use factoring.   

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

500

A rectangular prism has the volume of 16x³+34x²+4x. Factor to find the possible length, width, and height of the prism. v=l∙w∙h 

2x(8x+1)(x+2)