Polynomial Characteristics
Degrees and End Behavior
Extrema and Increasing/Decreasing of Polynomials
Operations with Polynomials
Factoring
100
Determine whether the function is even, odd, or neither. Explain your reasoning.
Even, because it is symmetric to the y-axis.
100
What is the degree of the following? Explain your reasoning.
f(x)= 3x - 5x2 + 8x4 - x3
4, it is the biggest exponent.
100
Where is the relative max?
(-2 , 3)
100
Add the following. Write your answer in standard form.
(2x3 - 4x + 5x2) + (3x2 - x + 3x3)
5x3 + 8x2 - 5x
100
Factor using GCF.
6x4 + 24x2
6x2(x2 + 4)
200
Is the leading coefficient of the following positive or negative? Explain your reasoning.
Positive, both endpoints are pointing up.
200
What is the degree of the following? Explain how you know.
Odd, endpoints are going in OPPOSITE directions.
200
Where is the relative minimum?
(0, 9)
200
Determine the difference. Write your answer in standard form.
(4x3 - 2x2 + 7x) - (x2 - 3x + 4x3)
- 3x2 + 10x
200
Factor by Magic X.
x2 - 11x + 30
(x - 5)(x - 6)
300
How many real zeros does this function have? Explain your reasoning.
4 real zeros, it crosses the x-axis 4 times.
300
Describe the end behavior of the following.
As x → - ♾️ , f (x) → - ♾️
As x → ♾️ , f (x) → ♾️
300
Determine the interval where the function is increasing.
1 < x < 3 and 4 < x < ♾️
300
Determine the product. Write your answer in standard form.
(x2 - 6)(x - 4)
x3 - 4x2 - 6x +24
300
Factor by Super Magic X.
2x2 + 3x - 9
(x+3)(2x - 3)
400
How many extrema does the following polynomial have? Explain your reasoning
3, there are three turning points. (2 minimums and 1 maximum)
400
Describe the end behavior of the following.
As x → - ♾️ , f (x) → ♾️
As x → ♾️ , f (x) → ♾️
400
Determine the interval where the function is decreasing.
-♾️ < x < 1 and 3 < x < 4
400
Determine the product. Write your answer in standard form.
(2x2 + 3x - 4)(x + 6)
2x3 + 15x2 + 14x - 24
400
Factor by Grouping.
12x3 - 21x2 + 28x - 49
(4x - 7)(3x2 + 7)
500
Does the following have an absolute maximum? Explain how you know.
No, there is only a relative maximum because the two endpoints go up forever.
500
Describe the end behavior of the following.
f(x)= 3x - 5x2 + 8x5 - x3
As x → - ♾️ , f (x) → - ♾️
As x → ♾️ , f (x) → ♾️
500
What do we call a function when it is neither increasing nor decreasing?
Constant. Flat horizontal line.
500
Divide the following. Hint: Use synthetic division.
(x3 - 2x2 - 14x - 5) by (x+3)
x2 - 5x + 1 - (8/x + 3)
500
Factor by the difference of cubes.
8x3 - 64y3
(2x - 4y)(4x2 + 8xy + 16y2)