Factoring
More factoring
Graphs
Sketch the graph
Simplify
Random product/factoring
More random polynomials
Graph and Analyze
100
Factor each completely.
x2 - 6x - 40
(x + 4)(x - 10)
100
Solve each equation.
4(1 + 3x) = -44
x = -4
100
What degree is the following Polynomial:
4
100
Sketch the graph of each line.
y = 5x + 1
m = 5
y-intercept = 1
100
Simplify
(5 - 6n4 - 2n3) + (8n3 - 2 + 2n4)
-4n4 + 6n3 + 3
100
Find each product:
(2x + 2)(2x + 7)
4x2 + 18x + 14
100
The degree of this polynomial:
x3 - 7x2 + 4x5 - 19x7
7
100
Find the zeros, multiplicities, y-intercept, end behavior, and estimated turning points.
f(x) = x(x - 2)
0, mult. of 1
2, mult. of 1
y-intercept: 0
local min (1, -1), No local max
As x -> (+) infinity, f(x) -> (+) infinity
As x -> (-) infinity, f(x) -> (+) infinity
200
Factor:
(x2 + 14x + 13)
(x + 1)(x + 13)
200
Solve the equation:
-3(1 + 8x) + 3x = 2(x + 8) - 4x
x = -1
200
What is the y- intercept?
y= x^3-4x^2-11x+30
30
200
Sketch the graph.
x - 2y = -6
m = 1/2
y - intercept: 3
200
Simplify
(5n3 + 5 + 5n2) + (7n2 + 2 - 7n3)
-2n3 + 12n2 + 7
200
Find each product:
(3m + 5)(4m2 - 2m + 4)
12m3 + 14m2 + 2m + 20
200
Find the zeros, multiplicity, and leading term:
Describe both the power and coefficient of the leading term:
f(x) = (x - 1)2(x + 1) (x - 3)
zeros: 1, -1, 3
Multiplicities: 2, 1, 1
Leading term: x4
Positive and even
200
State the degree, classification, power term, and end behavior of the following.
f(x) = 3x2 + x - 1
Degree: 2
P. Term: 3x2
Quadratic
As x -> (+) infinity, f(x) -> (+) infinity
As x -> (-) infinity, f(x) -> (-) infinity
300
Factor:
(7x2 + 3x - 5)
(7x - 4)(x + 1)
300
Solve each equation by factoring.
x2 + 11x + 30 = 0
x = -5, -6
300
What is the End Behavior of this graph?
Left -> Down ; Right -> Up
OR
As x -> (-) Infinity, f(x)-> (-) Infinity
As x -> (+) Infinity, f(x)-> + Infinity
300
Sketch the graph.
x + y = -1
m = -1
y-intercept = -1
300
Simplify
(2x2 - 6x4 + 2x3) - (6x4 - 2x2 + 4x3)
-12x4 - 2x3 + 4x2
300
Find each product:
(5x2 - 7x + 8)(5x2 + 3x + 6)
25x4 - 20x3 +49x2 -18x + 48
300
What happens when the multiplicity is even and odd?
even -> bounces
odd -> crosses
300
How do you find the y-intercept of a polynomial function graph?
Set x = 0
400
Factor each completely:
4x2 - 4x - 15
(2x + 3)(2x - 5)
400
Solve each equation by factoring:
7x2 - 6x - 8 = -8
x = 0, 6/7
400
How many Min and Max does this graph have?
2 Local Max ; 1 Local Min
400
y = -2(x - 4)2 +2
Horizontal shift: 4
Vertical shift: 2
Reflection across x-axis
Vertical Stretched
400
Simplify
(6 + 6x + x2) - (5 - 6x2 - 8x)
7x2 + 14x + 1
400
Find each completely:
6x3 - 9x2 - 2x + 3
(2x - 3)(3x2 - 1)
400
What are the Zeros and their Multiplicity?
x= -5 , Mult. 1
x= -1 , Mult. 1
x= 3 , Mult. 2
400
Find the zeros, y-intercept, end behavior, and how many relative min/max points
f(x) = -x2(x + 2)(x + 4)
Zeros: 0, multi. of 2
Zeros: -2, multi. of 1
Zeros: -4, multi. of 1
y-intercept : 0, 1 min and 1 max point
As x -> (+) infinity, f(x) -> (-) infinity
As x -> (-) infinity, f(x) -> (-) infinity
500
Factor by grouping:
4x3 - 6x2 - 2x + 3
(2x - 3)(2x2 -1)
500
Solve each equation by factoring.
2x2 - 9x = 18
x = -3/2, 6
500
Classify the function.
Degree of 4
Quartic
500
Sketch the graph.
y = (x - 3)2 - 4
Horizontal shift: 3
Vertical shift: down 4
No reflection across x-axis/y-axis
No vertical compression or stretch
500
Find each product:
(2r - 4)(6r + 2)
12r2 - 20r - 8
500
Solve each by factoring:
7x2 - 16x + 2 = -2
x = 2/7, 2
500
Using the leading term, find the degree, classify and determine the end behavior of each polynomial function:
f(x) = 3x5 + 4x2 +7x + 2
LT: 3x5
Degree: 5
Quintic
As x -> (+) infinity, f(x) -> (+) infinity
As x -> (-) infinity, f(x) -> (-) infinity
500
Determine the zeros, multiplicity, y-intercept, end behavior, and how many relative min/max points.
f(x) = x(x + 2)(x - 2)(x - 4)
Zero 0, multi. of 1
Zero -2, multi. of 1
Zero 2, multi. of 1
Zero 4, multi. of 1
y-intercept = 0, 2 min points & 1 max point
As x -> (+) infinity, f(x) -> (+) infinity
As x -> (-) infinity, f(x) -> (+) infinity