End Behavior...& Other Poly Characteristics!
The end behavior of f(x)=.4x2-.02x3+x+1.
What is...
as x appr. -infinity, f(x) appr. infinity
and
as x appr. infinity, f(x) appr. -infinity
Find ALL roots of the equation x3-x=0.
x = -1, 0, 1
Divide using synthetic division.
(x3-x2-63x-47)/(x+7)
x2-8x-7 + 2/(x+7)
Graph an exponential function
check your notes
Write an equation for a polynomial function that snakes thru (-1,0), bounces at (3,0), and rises left and falls right.
What is f(x)=-(x+1)3(x-3)2?
What is the degree and what vocabulary word is used for that degree?
h(x)=x5-4x3+9x2-1.
5 - Quintic
Factor to find the zeros of f(x)=x4-10x2+9
x = -3. -1. 1, 3
Divide using synthetic division.
(-41x+7x2+3x3-5)/(x+5)
3x2-8x-1
Find all real roots of f(x) and state the multiplicity of each.
f(x)=x3-x2-5x-3
x = 3 - Simple mult. of 1
x = -1 - Even mult. of 2
Write the factored form equation for the polynomial function that passes thru (0,0), bounces at (-5,0), rises to the right and falls to the left
f(x)=x(x+5)2
If y=-8x9+9x2-x+15, then there are at most ___ zeros
What is "9"?
All of the zeros of the function y=x2- 9x+18.
What are x =6, 3
Divide using synthetic division.
(b4+10b3+31b2+36b+15)/(b+3)
b3+7b2+10b+6 - 3/(b+3)
Write the quadratic that has been shifted left 3, down 2, and reflected across the y axis
y = - (x+2)2 - 2
Write the factored form equation for the polynomial function that passes thru (-5,0), snakes thru (5,0) and whose end behavior is - inf and -inf
f(x)=-(x+5)(x-5)3
If y = x3 - 4x - x2 + 4 then the zeros are
-2, 1, 2
List all of the possible rational zeros of f(x)=-3x5+6x2-7.
What are x = -1, 1, -7, 7, -1/3, 1/3, -7/3, 7/3?
Use synthetic division to prove x+4 is a factor of f(x).
f(x)=x5+4x4+9x3+36x2
f(x)=(x+4)(x4+9x2)
Given that f(x)=2x3-7x2-46x-21 passes thru (-7,0), find all of the zeros
x = 7, -1/2, -3
Write the simplified form of the equation for a polynomial function that bounces at the origin and has zeros at 3 and -2
f(x) = x4 - x3 - 6x2
The factored form of the polynomial 27x4-8x.
What is x(3x-2)(9x2+6x+4)?
Find all zeros of f(x)=4x3-3x-1
Factors: (2x+1)(2x-1)(x-1)
zeros: -1/2, 1/2, 1
Divide using long division. :)
(-4x3+8x2-11x-140)/(2x+5)
-2x2+9x-28
Find all the factors of f(x)=x4+4x3+x2- 6x
Factors: x (x+3)(x+2)(x-1)
Write the simplified form of the equation for a polynomial function that bounces at the origin and has zeros at 4, -6, and -4
f(x) = x5 +6x4 -16x3 - 96x2