Operations
Factoring/Solving
Graphs
Functions
Basics
100
Add:
(5x - 4) + (x2 - 9)
x2 + 5x - 13
100
Factor:
x2 + 15x + 56
(x + 7)(x + 8)
100
What are the roots of the given function?
(-5,0), (-4,0), (-1,0), and (1,0)
or
x = -5, -4, -1, and 1
100
Solve for the value of the given function:
f(x) = x2 + 3x - 20, when we have f(-1).
f(-1) = -22
100
Classify this polynomial:
-7b4 + 2b
Quartic Binomial
200
Subtract:
(4x2 - 5x + 3) - (-5x2 - 9x + 5)
9x2 + 4x - 2
200
Factor:
3x2 + 11x + 10
(x + 2)(3x + 5)
200
Identify the relative extrema:
a, b, and d
200
Given f(x) = x2 - 2x - 48 and g(x) = x - 8.
Find (f + g)(x).
(f + g)(x) = x2 - x - 56
200
Given the polynomial below
1/7-7x^2+5x^4+x^5-8x
Determine the
Degree:
Leading Term:
Constant Term:
Degree: 5
Leading Term: x5
Constant term:
1/7
300
Multiply:
(2x + 3)2
4x2 + 12x + 9
300
Solve:
x3 - 6x2 - 72x = 0
x = -6, 0, 12
300
Determine the end behavior:
C.
As x goes to negative infinity, f(x) goes to positive infinity.
As x goes to positive infinity, f(x) goes to negative infinity.
300
Given f(x) = 2x2 - 4x + 7 and g(x) = 5x - 3.
Find (f - g)(3)
(f - g)(3) = 1
300
Why is the given polynomial not a true polynomial?
2x+3/x-x^2
There is a variable in the denominator.
400
Divide:
(3x^4-15x^3+21x^2)/(3x^2)
x2 - 5x + 7
400
Solve:
4x2 - 49 = 0
x=-7/2,7/2
400
Create a function from the roots of the graph:
f(x) = (x - 4)(x - 4)(x - 6)
or
f(x) = (x - 4)2(x - 6)
400
Given f(x) = x + 12 and g(x) = x2 - 2x - 15
Find g(f(-5))
g(f(-5)) = 20
400
Place in standard form:
2ab+a^3-b+7a^2b^2-1
7a^2b^2+a^3+2ab-b-1
500
Divide:
x3 - 10x2 + 21x - 1 divided by x - 2
x^2-8x+5+9/(x-2)
500
Solve:
3x3 - 25x2 + 6x = -6x2
x(x - 6)(3x - 1)
x = 0, 6, 1/3
500
Determine the domain on which the function is increase AND decreasing.
Decreasing:
(-oo, 2)
Increasing:
(2,oo)
500
Given f(x) = x2 - 3x + 12 and g(x) = 5x + 8
Find (f o g)(x)
(f o g)(x) = (5x + 8)2 - 3(5x + 8) + 12
or
(f o g)(x) = 25x2 + 65x + 52
500
Place in standard form:
5+x^2-xy+13x^4y^3-6x^2y^3z^2
13x^4y^3-6x^2y^3z^2+x^2-xy+5