Factoring
Quadratics
Polynomials
Radicals
Rationals
100

Factor 3a2+9a

3a(a+3)

100

What is the vertex of a graph with the equation y=-2(x+1)+1

(-1,1)

100

What is the end behavior for the function f(x) = -2x4 + 8x3 - 8x2 + 2

x-->-infinity, f(x)-->-infinity

x--> +infinity, f(x)-->-infinity

100

Simplify: cube root of (a6b9)

a2b3

100
In how many different ways can five students be seated in three chairs?
60. 5x4x3=60
200

Factor completely: a2-25

(a+5)(a-5)

200

Find the quadratic model for the given data to the nearest thousandth. Use 1981 as year 0.

(1981,18), (1991, 29), (1995, 32), (1999,33), (2001, 34), (2006, 39), (2007, 41), (2008, 42)

y=-0.0025x2+0.8986x+18.6639

200

What is a cubic polynomial function in standard form with zeros -2,2 and 3?

f(x) = x3 - 3x2 - 4x + 12

200
The cost of admission to an event is $5.00 plus one half of its price. How much does the event cost?
$10.00 Because $5 + 0.5($10) = $10.
300

Factor completely: x2+5x+6

(x+3)(x+2)

300

Solve the following 3x2 - x - 2 = 0

x=1, x=-2/3

300

Solve the following polynomial x4 - 3x2 = 4.

x = 2, x = -2, x = i, x = -i

300
Simplify (x + 2)^2 - x^2
4(x+1) Note: x^2 + 4x + 4 - x^2
300
Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads OR all will come up tails?
1/4. 1/8 (all heads) + 1/8 (all tails) = 1/4.
400

Factor the GCF then factor completely: 27p2-9p+18

9(3p - 2)(p - 1)?

400

What is the value of the discriminant and what does it mean about the nature of the solutions 

4x2-2x=10

b2-4ac = 164

This means there are 2 real solution

400

Given the function q(x) = 2x4 - x3 - 35x2 +16x +48, determine if x+1 is a factor and explain your method.

x+1 is a factor. Possible methods are long division or synthetic division and no remainder or the remainder theorem evaluated to 0.

400
For the system of three equations: x-z=7, x+y=3, z-y=6, what is x?
8
400
Five students, all of different heights, are randomly arranged in a line. What is the probability that the tallest student will be first in line and the shortest student will be last in line?
1/20. 1x3x2x1x1=6, 6 ways in which students can be arranged under given conditions. Under no conditions, the ways are 5x4x3x2x1=120. 6/120=1/20.
500

Factor: x3+3x2+4x+12

(x2+4)(x+3)

500

A parabola has a focus at (1,2) and its directrix is y=-2. What is the equation of this parabola?

y=1/8(x-1)2

500

Find the quotient and remainder (2x3+9x2+11x+3)/(x+2)

2x2+5x+1 + 1/(x+2)
500
For how many integer values of b is b+3>0 and 1>2b-9?
Seven. b>-3, and b<5. Since b is an integer, b may be equal to any of the following: -2, -1, 0, 1, 2, 3, or 4.
500
x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?
32. x=70, y=38. 70-38=32.
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