End Behaviors and more
Degree and Leading Coefficient
Adding & Subtracting Polynomials
Polynomials Long Division
Long Division and more
100
Identify the end behavior of the following graph:
As x → -∞, _________
x → ∞, __________
As x → -∞, f(x) → ∞
x → ∞, f(x) → ∞
100
What is the degree and Leading Coefficient:
5k2 + 6k3 -4jk
Degree: 3
Leading Coefficient: 6
100
Simplify:
(4x + 9) +(x - 4)
5x + 5
100
Divide:
15x^2 - 5x
15x - 5
100
What are like terms?
Terms with the same variable and the same exponent.
200
Identify the end behavior of the following graph:
As x → -∞, _________
x → ∞, __________
As x → -∞, f(x) → ∞
x → ∞, f(x) → -∞
200
Find the degree and leading coefficient of this polynomial:
x3 - 7x2 + 4x5 - 19x7
Degree: 7
Leading Coefficient: -19
200
Simplify
(x2 +3x + 5) + ( -x2 +6x)
9x + 5
200
Divide:
(8x^3 - 4x^2 + 12x) / (4x)
2x^2 - x +3
200
The number before a variable within a term is called the...
Coefficient
300
Using graphing technology, determine the following key features for the function:
f(x) = -3x^4 + 2x^2
-The function f(x) is: a) even b)odd c)neither
-The left end behavior can be described as x → -∞,
-The right end behavior can be described as x → ∞,
-The function is EVEN
-Left end behavior: as x → -∞, f(x) → -∞
-Right end behavior: as x → ∞, f(x) → -∞
300
Given the graph of this polynomial, what do we know about the leading coefficient?
a) Positive leading coefficient
b) Negative leading coefficient
c) No leading coefficient
d) Cannot be determined
A) Positive leading coefficient
300
If
f(x) = 3x^2+5x - 3
and
g(x) = x^2 + x - 4
What is the simplified expression for f(x) + g (x)?
(f + g) (x) = 4x^2+6x-7
300
Divide
(2x^3+5x^2+18x+45)/(2x-5)
x^2 + 9
300
One solution to this polynomial is x=-4. Find the other 2 solutions.
f(x)=x^3+4x^2-9x-36
Quotient: x2-9
Other solutions:
400
Using graphing technology, determine the following key features for the function:
f(x) = -x^7+4x^2
-The function f(x) is: a) even b)odd c)neither
-The left end behavior can be described as x → -∞,
-The right end behavior can be described as x → ∞,
-The function is ODD
-Left end behavior: as x → -∞, f(x) → ∞
-Right end behavior: as x → ∞, f(x) → -∞
400
Determine if the function graphed has an odd or even degree AND a positive or negative leading coefficient.
Degree: Odd
Leading Coefficient: Positive
400
If
f(x)= 2x^2 - 7x - 5
and
g(x) = x^2 - x + 5
What is the simplified expression for f(x) - g (x)?
(f-g)(x)= x^2 - 6x - 10
400
A student performed the following division. The work of the student is all correct.
Is x-1 a factor of 8x3 - 10x2 - x + 3?Yes o No? Explain how do you know.
Yes, (x+1) is a factor, there is no remainder, so the original polynomial can be written as (x-1) (8x2-3x-3)
400
One solution to this polynomial is x=-1. Find the other 2 solutions.
f(x) = x^3+x^2-10x-10
Quotient: x2-10
Other solutions: 
500
Using graphing technology, determine the following key features for the function:
f(x) = -x^5+5x^2
-The function f(x) is: a) even b)odd c)neither
-The left end behavior can be described as x → -∞,
-The right end behavior can be described as x → ∞,
-The function is ODD
-Left end behavior: as x → -∞, f(x) → ∞
-Right end behavior: as x → ∞, f(x) → -∞
500
Determine if the function graphed has an odd or even degree AND a positive or negative leading coefficient.
Degree: Even
Leading Coefficient: Positive
500
If
f(x)=2x^2 + 4x - 8
and
g(x) = x^2 + 2x + 4
What is the simplified expression for f(x) - g (x)?
(f-g) (x)=x^2+2x -12
500
Divide:
(6x^2+12x)/(3x)
Is your result a factor of the polynomial? Yes or No? Explain how do you know.
Quotient: 2x+4
Yes, (2x+4) is a factor, there is no remainder, so the original polynomial can be written as (3x) (2x+4)
500
One solution to this polynomial is x=2. Find the other 2 solutions.
f(x)= x^3-2x^2-7x-14
Quotient: x2-7
Other solutions: 