Polynomial Division
Zeros of Polynomials
Rational Functions
Variation
Exponentials
100
What are the two ways to divide polynomials?
Long division and Synthetic division
100
In the Rational Root Theorem, P represents all of the factors of the constant term, all the factors of the leading coefficient, or all of the possible rational roots?
All the factors of the constant term
100
What does "rational" mean in math?
A fraction
100
If y varies directly as x, and x=9 when y=27, find y when x =10.
y=30
100
How can you tell if a function is an exponential?
If it is has a variable as an exponent
200
What condition is required in order to be able to use synthetic division?
The degree of the divisor must be 1
200
How many possible positive real roots are there for the polynomial below?
f(x) = 3x4-5x3+3x-7
3 or 1
200
How do you find the vertical asymptotes of a rational function?
Set the denominator equal to 0 and solve.
200
If z varies directly with the square root of t, and z = 16 when t = 64, then find z when t = 100
z=20
200
A the population of trees in a particular forest is given by the function P(t) = 100*(1.2)t, where P(t) is the population and t is the time in years. What is the starting population of trees in the forest?
100 trees
300
If you were using synthetic division to divide the polynomials below, what number would go in the box, and what would be the row of numbers next to the box?
(5x^4-4x^3+6)/(x-6)
In the box: 6
Row: 5 -4 0 0 6
300
What are the possible rational roots for the polynomial below?
f(x) = 2x5-6x2+10x-3
+/- 1
+/- 3
+/- 1/2
+/- 3/2
300
Given the rational function below, where would the hole be located and where would the zero be located?
(x^2+x)/(x)
Hole at x=0 and zero at x=-1
300
If y varies inversely as x, and y = 6 when x = 3, then find y when x = 9
y = 2
300
A the population of trees in a particular forest is given by the function P(t) = 100*(1.2)t, where P(t) is the population and t is the time in years. What will the population of the forest be in 5 years?
About 249 trees
400
Divide
(x^2+2x+1)/(x+1)
x+1
400
How many possible negative real roots are there for the polynomial shown below?
f(x) = 10x7-x5+10x3-5
2 or 0
400
For the rational function below, state the horizontal asymptote and vertical asymptotes.
(5x)/((x-4)(x-3))
HA is y=0 and VA are x=3 and x =4
400
The current in a simple electrical circuit is inversely proportional to the resistance. If the current is 8 amps when the resistance is 5 ohms, find the current when the resistance is 40 ohms.
1 amp
400
Write the equation of the exponential that passes through the points (0,5) and (2, 20)
y=5*2x
500
What is the remainder of the division problem shown below in fraction form?
(2x^2-3x+4)/(x-2)
6/(x-2)
500
You perform synthetic division on a polynomial and get the result pictured below. What are the three roots of the polynomial?
x=1, x=2, x=3
500
A rational function has vertical asymptotes at x=4 and x=-2, a zero at x=8, and a y-intercept at (0,4). Write an equation that represents the function.
f(x)=(4(x-8))/((x+2)(x-4))
500
If f varies jointly as g and the cube of h, and f = 80 when g = 5 and h = 2, find f when g = 3 and h = 1
f=6
500
How much money would be in an account after 20 years if the initial deposit was $100,000, the annual interest rate was 5%, and the interest was compounded continuously?
About $271,828