Classifying Polynomials
How do we classify(name) polynomials?
By their degree and the number of terms
Even functions are symmetric about the
Y-axis
Translate the following
As x --> - ∞, y --> - ∞,
As x approaches negative infinity, y approaches negative infinity
Odd functions are symmetric about a specific point, which we call the
origin
4x2 + 4x - 11
Write in Standard Form, Classify the polynomial by degree and terms.
7x3 - 10x5 - 1
-10x5 + 7x3 - 1
Quintic Trinomial
Determine if the following function is even, odd, or neither.
f(x) = - x3 - 10x + 1
Neither
What is the end behavior of p(x) = x2 - x + 10
As x --> - ∞, y --> ∞,
As x --> ∞, y --> ∞
Name the zeros, multiplicity and effects of the following polynomial? f(x) = x4 - 16x3 + 64x2
x2(x2 - 16x + 64) = x2(x - 8)(x - 8) =x2(x - 8)2
zeros: 0, 8
Multiplicity: 2, 2
Effect: bounces, bounces
(2a2b - 5b3 + 4a4b2) - (7b3 + 8a4b2 - 7a2b)
- 5b3 - 7b3 + 4a4b2 - 8a4b2 + 2a2b + 7a2b
- 4a4b2 + 9a2b - 12b3
Classify the polynomial.
g(x) = -5x9 + 10x4
9th degree binomial
If both arrows are pointing down, is it an even or odd degree polynomial? Also, describe the leading coefficient as + or -.
Even, negative
If the left arrow is pointing up and the right arrow is pointing down (see graph on board) is this an even or odd degree? What is the leading coefficient?
See graph on board
Odd degree, negative leading coefficient
What is the degree of the following polynomial?
g(x) = 11x2 - 5x4 + 5(x3 + x4) - 1
Degree 3
5c-7d2 * (-cd2)4
5d10
c3
Classify the following polynomial
g(x) = -4x2 - 10 + 5 - 2(-2x2)
-5
Constant monomial
Determine if the following is even, odd, or neither
S(x) = x9 - x3 + x
Odd
Describe the end behavior of the following function.
S(x) = -6x7 - 10x4 - 1
As x --> - ∞, y --> ∞,
As x --> ∞, y --> - ∞,
If the degree of the function is even, the arrows will point in ______ directions, if it is odd, the arrows will point in _____ directions.
(Different or The same)
f the degree of the function is even, the arrows will point in THE SAME directions, if it is odd, the arrows will point in DIFFERENT directions.
15x2y * -6x7y
(3xy)2
-90x9y2
9x2y2= -10x7
Write in Standard form, Classify the polynomial with degree and terms
L(x)= x3 - (x2 + 3x + x3) - 7x5
x3 - x2 - 3x - x3 - 7x5
-7x5 - x2 - 3x
Quintic Trinomial
-7x5 - x2 - 3x
Even, odd, or neither
p(x) = 6x16 - 10x6 - 3
Even
Describe the end behavior of g(x).
g(x) = 2x - 6x9 + 20 - 5x
As x --> - ∞, y --> ∞,
As x --> ∞, y --> - ∞,
Even Odd or Neither
p(x) = 3x - 10 + 5x2
Neither
(1 - 2n)3 - 7n(n2 - 2)
-15n3 +12n2 + 8n + 1