Inequalities
Factoring Polynomials
Word Problems
Graphing Polynomials
and Rationals
Finding Asymptotes
and Holes
100

*TRICK

The leading term of the following polynomial 

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



What is 144x6

100

x3+7x2+16x+12

(x+2)2(x+3) 

100

Colin and Sean are making the largest cup of tea in the world. There is already 405 gallons of tea and 15 pounds of sugar. Colin is adding sugar at 3 pounds/minute while Sean is pouring tea at 135 gallons per minute. Write a function that represents pounds/gallon with x as minutes.

f(x)=3x+15/135x+405

100

Graph (x^2-4)(x-1)^2/x-2


(see image)

100

what are the asymptotes of

 1/x + 2

Vertical at x=0

horizontal at y=2

200
x2+x-8 <-2

What is (-3,2)

200

x2+3x-4

(x+4)(x-1)

200

Colin and Sean are making the largest cup of tea in the world. There are already 405 gallons of tea and 15 pounds of sugar. Colin is adding sugar at 3 pounds/minute while Sean is pouring tea at 135 gallons per minute. What is the sugar to tea ratio after 10 minutes?

1/39

200

x/[(x+1)(x-3)]

see image 2

200

[2x2-5x+2]/[x2-4]

vertical at x=-2

horizontal at y=2

300

(x+2)² < 0

No solution

300

x3+4x2-4x-16

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

300
The concentration of a medicine in a patient's bloodstream f over hours x is represented in the function f(x)=x+1/2x^2+5. What is the concentration of the medicine after 2 hours? 

0.231

300

(x2-x-12)/x

see image 3

300

where is the hole

[x2+4x+3]/[x2+8x+15]

hole at x=-3


400

x2+3x-6 ≤ -2

[-4,1]

400

Find the standard form of the following equation (x+2)2 (x+3)

What is x3+7x3+16x+12

400

A company hired you to design a closed rectangular prism-shaped packaging box. The box has to be 10000 cm^3 in volume. Express the amount of material required to make the box as S and x as the side length of the base. What is the side length in terms of x?

S=x^2+4x(10000/x^2)

400

(x2-3x-4)/(x+4)

see image 4

400

find the asymptotes   

[(x+5)(x+8)]/[(x+2)(x+4)]

vertical at x=-4,-2

horizontal at y=1

500

(2x2-4x-6)/(x3-4x2+3x)≥ 0

(-1,0)U(1,∞)

500

2x2+7x+3

(2x+1)(x+3)

500

Water coolers made for sports are made in cylindrical barrels. The coolers have to hold at least 3 cubic feet of water. Express the amount of materials M needed in terms of the radius r of the base. What is the value of r to minimize the amount of material required? (Calculator/Desmos required)

Function: 2πr^2+2πr*3/πr^2

The radius for minimum cost: 0.782

500

(x4+2x3-7x2-8x+12)/(x2+2x+3)

image 5
500

find the hole and asymptotes

[(x+3)/x2 +8x+15]+1

hole x=3

vertical asymptote x=-5

horizontal asymptote y=1

M
e
n
u