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)
List the possible rational roots.
f(x)=5x3+17x2+26x+8
x = +/- 1, 2, 4, 8, 1/5, 2/5, 4/5, 8/5
Write an equation for a polynomial function that snakes thru (-1,0), bounces at (3,0), and rises right and falls left.
What is f(x)=2(x+1)3(x-3)2? *Any positive LC will work!
The y-intercept of h(x)=x5-4x3+9x2-1.
What is (0,-1)?
Factor to find the zeros of f(x)=x4+4x2+3
x = i, -i, i√3, -i√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), and also contains the point (-4,-12).
f(x)=3x(x+5)2
If y=-8x9+9x2-x+15, then as x increases, y ______.
All four zeros of the function y=x4-9x2+18.
What are x = √6, -√6, √3, -√3?
Divide using synthetic division.
(b4+10b3+31b2+36b+15)/(b+3)
b3+7b2+10b+6 - 3/(b+3)
Find all real roots using PRZ's, synthetic division, and factoring.
f(x)=x3+9x2-21x+11
x = 1, 1, -11
Write the factored form equation for the polynomial function that passes thru (-5,0), snakes thru (5,0), and f(0)=625.
f(x)=-(x+5)(x-5)3
A 5th-degree polynomial function has at most _______ x-intercepts and at least _______ of them.
What is "5" and "1"?
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)=x3+11x2+26x-14 passes thru (-7,0), find all remaining zeros of the function.
x = -2-√6 & -2+√6
Write the factored form equation for a least degree polynomial function that bounces at the origin and has an imaginary zero x=4i. There are many possible answers.
f(x)=x2(x2+16)
The factored form of the polynomial 27x4-8x.
What is x(3x-2)(9x2+6x+4)?
This polynomial function snakes thru (-1,0), bounces at (3,0), and rises left and falls right.
f(x)=-(x-3)2(x+1)3 *Any negative LC will work!
Divide using long division. :)
(-4x3+8x2-11x-140)/(2x+5)
-2x2+9x-28
Find all zeros of f(x)=4x3-3x-1 using PRZ's, synthetic division, factoring, etc.
x = 1, -1/2, -1/2
Multiply (x-(1-3i))(x-(1+3i)).
x2-2x+10