Radical Equations
Rational Equations
Remainder Theorem
Factor Theorem
Polynomial Equations
Word Problem Grab Bag
100

1. The graphed functions 

2. The window used. 

3. The calculator function used to find the answer. 

4. The answer.

What are the four requirements for a graphical solution on a test?

100

Extraneous values

What is the name for algebraically-derived solutions that are not actual solutions to the equation?

100

 P(a) , for some polynomial  P(x) 

What is the remainder of  (P(x))/(x-a) ?

100

If  P(a) = 0 for some polynomial  P(x) .

When is  (x-a) a factor of  P(x) ?

100

How you can find factors of  P(x)  from the graph y=P(x) .

What are the x-intercepts of the graph  y=P(x) ?

100
A kite is secured to a rope that is tied to the ground. A breeze blows the kite so that the rope is taut while the kite is directly above a flagpole that is 30m from where the rope is staked down. Find the altitude of the kite if the rope is 110m long.
The kite is 105.8m from the ground. 
200

sqrt(x+4)=7

x=45

200

5/(x-2)=7

x=1

200

The remainder of 

(x^3+2x^2-6x-7)/(x-1)

 P(1) = (1)^3+2(1)^2-6(1)-7 

P(1) = -10

200

The best choices for  a when factoring  P(x) by factors of  (x-a) .

What are integral factors of the constant term in  P(x) ?

200

Solve 

x^3-19x-30=0

x=5, -2, -3

200

A 12m tall tree was broken into two parts. It was found that the height of the cut part was related to the remaining length by the formula x^3+x-10=0.

Determine the length of the cut piece (x).

The length of the cut piece was 2 m.

300

sqrt(2x+3)=5

x=11

300

(3x)/(x+4)=2

x=8

300

The division of 

(x^3+4x^2-3x+5)/(x+2)

(x^2+2x-7) + 19/(x+2)

300

The factors of  x^3+5x^2+7x+3.

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

300

Solve

6x^3-10x^2-4x+8=0

x=1, (1+-sqrt(13))/3

300

The speed of a tsunami (in  m/s ) is related to the depth of the ocean in meters by the formula

 v=sqrt(9.8d) 

Determine the depth of the ocean when the speed is 117 m/s .

The ocean's depth would be 1396.84m.

400

sqrt(4x+5)=x

 x=5 

 x=-1 is extraneous.

400

(4x+3)/(x+2) = 9/5

x=3/11

400

The division of  (x^4+3x^3-5x^2-2x+120)/(x+5) 

(x^3-2x^2-5x+23)+5/(x+5)

400

One factor of 

x^4-x^3-7x^2+x+6

(x-3)

(x+2)

(x-1)

(x+1)

400

Solve 

2x^4+x^3-8x^2-x+6=0

x=3/2,1,-1,-2

400

Lisa can paint a room in 6 hours, whereas her sister Jessica can paint the same room in 4 hours. How long would it take both sisters to paint 3 rooms?

It would take 7 hours and 12 minutes to paint 3 rooms.

500

sqrt(2x-7)=x-5

 x=8 

 x=4 is extraneous.

500

3x-32/(x-4)=2x

 x=8,-4 

500

The remainder of  (5x^5+3x^3+4x^4-1)/(x+3) 

x=-973

500

One factor of  3x^4+8x^3-40x^2-28x-15 .

 (x+5) 

(x-3)

(3x^2+2x+1)

500

Solve 

2x^4-7x^3-15x^2+56x-48=0

x=4,-3

500

Kaiden walks 15 km and bikes 120km. If he bikes 20km faster than he walks, and the total trip takes 12 hours, determine Kaiden's walking speed.

Kaiden walks at 2.27 km/h.

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