Degree
What is the degree of the following polynomial and what form is this polynomial in?
f(x) = -2x4 - 5x2 + 3x - 10
Degree: 4; Standard Form
What is an extrema?
turning points of a polynomial
if a polynomial's end behavior is the same the function has this type of degree
Even polynomials
The roots and multiplicities of
f(x) = (x-2)(x+3)
What is 2 mult 1, -3 mult 1
Go to desmos.com/calculator and identify ONE interval of increase of the polynomial: f(x) = x(x-1)(x+2)2
What is the degree of the following polynomial and what form is this polynomial in?
f(x) = 10x3 + 3x - 10
Degree: 3; Standard form
Go to desmos.com/calculator and identify ONE extrema of the polynomial:
f(x) = -(x+1)(x+3)2
Label the point as (relative min/max, absolute min/max) and the ordered pair.
Relative (local) max: (-1.7, 1.2)
Relative (local) min: (-3,0)
If the polynomial is odd then this happens to the end behaviors
What is they are different
When a root has an even multiplicity what occurs at that root on the x-axis?
It bounces
Go to desmos.com/calculator and identify ONE interval of decrease of the polynomial: f(x) = x(x-1)(x+2)2
(-inf, -2) OR (-0.8, 0.6)
What is the degree of the following polynomial and what form is this polynomial in?
f(x) = (x+3)4(x-1)2
Degree: 6; Factored form
Go to desmos.com/calculator and identify ONE extrema of the polynomial:
f(x) = -x4 + 3x3 - 2x
Label the point as (relative min/max, absolute min/max) and the ordered pair.
Abs Max: (2.1, 4.1)
Rel (local) Max: (-.4, .5)
Rel (local) Min: (.5, -0.7)
If the polynomial is even and the lead coefficient is negative then the end behaviors
What is are both down
What are the roots and multiplicities of f(x) = x(x-1)3?
x = 0 mult 1, 1 mult 3
Go to desmos.com/calculator and identify ONE interval of increase of the polynomial: f(x) = x(x+2)2
(-inf, -2) OR (-0.7, inf)
What is the degree of the following polynomial and what form is this polynomial in?
f(x) = x(x-5)(x+2)3
Degree: 5; Factored Form
Even
If the left end is down and the right end is up, the degree is___ , and the leading coefficient is ____
What is odd, positive
x = -4, 1
Go to desmos.com/calculator and identify the interval of decrease of the polynomial: f(x) = x(x+2)2
(-2, -0.7)
How do you find the degree of a polynomial in factored form?
Add up the exponents (multiplicities) of the factors.
Go to desmos.com/calculator and identify ONE extrema of the polynomial:
f(x) = (x+4)3(x-1)
Label the point as (relative min/max, absolute min/max) and the ordered pair.
Abs min: (-0.3, -65.9)
What are the roots and multiplicities of the polynomial
f(x) = -x(x-5)(x+3)(x-1)2
x = 0 mult 1, 5 mult 1, -3 mult 1, 1 mult 2
Go to desmos.com/calculator and identify ONE interval of decrease of the polynomial: f(x) = x(x+2)3
(-inf, -0.5)