Factors
What are the factors of x2 - 6x - 72
(x - 12)(x + 6)
what two parts of a polynomial equation gives you the end behavior?
leading coefficient and degree
what is the name of the following function y=2x2+8x-4x3?
cubic trinomal
what are two other names for roots?
zeros, x-intercepts
What is the Vertical Asymptote of the function: (2x - 3)/(x - 4)?
What is x = 4?
factor 6x2+x-2
(2x-1)(3x+2)
what is the end behavior of the function f(x)= -2x3-4x-9?
as x approaches +infinity, f(x) approaches -infinity as x approaches -infinity, f(x) approaches +infinity
give an example of a 4th degree polynomial with a negative leading coefficient.
y= -x4 (multiple answers)
how can you determine how many roots a polynomial should have?
the total number of zeros/solutions/roots matches the degree of the polynomial
What is the Horizontal Asymptote of the function: (2x - 3)/(x - 4)?
What is y = 2?
what are the factors of x2-144
(x+12)(x-12)
what is the end behavior of a 5th degree polynomial function with a negative leading coefficient and 3 real roots?
as x->inf, f(x)->-inf; as x->-inf, f(x)-> inf
Give an example of a polynomial function whose degree is 3 and has a negative leading coefficient
y=-x^3
what is/are the solution/s of the polynomial equation f(x) = x3+3x2+3x+1
x= -1
Define the hole in the function: (x2 - 64)/(x2 + 9x + 8)
What is (-8, 16/7)?
Which of the following polynomial functions has (x-5) as a factor?
a. 2x3 + 10x2 - x - 5
b. x2 + 4x + 5
c. 5x3 + 20x2 + 25x
d. 2x3 - 10x2 + x - 5
d. 2x3 - 10x2 + x - 5
Is the leading coefficient of the following polynomial negative or positive and explain how you know?
2x3 - 10x4 + x + x2 - 5
negative because when written in standard form, the leading coefficient is negative (-10)
What is the end behavior of the function g(x) = -4x4 + 3x3 - 4x + 3
What is as x--> +infinity, f(x)--->- infinity as x--> - infinity, f(x) --> - infinity
What are the zeros of x3 - 5x2 + 2x - 10
x= 5, +sq rt (2i) and -sq rt (2i)
Identify the x and y intercepts in the function: (a - 4)/(2a - 8)
What is (0, 1/2) and (4, 0)?
double jeopardy!! answer both questions
1) what are the factors of 3x2 + 4x - 4
2) what are the factors of -x4 + 4x3 - 4x2
(3x - 2)(x + 2)
-x2(x - 2)(x - 2)
What is the end behavior of an odd function with a positive leading coefficient?
What is as x--> +infinity, f(x)--> + infinity as x--> -infinity, f(x)--> - infinity
Tell the end behavior, leading coefficient, degree, Number of terms, and how many roots the function h(x)=2x3+5x2-6x-1
What is a third degree (cubic) with 4 terms, 3 roots, and a positive LC.
Write a polynomial in factored form whose zeros include x = 1, x = 1 + 2i, x = 1 - i.
f(x) = (x - 1)(x - (1 + 2i))(x - (1 - 2i))(x - (1 - i))(x - (1 + i))
Given f(x)=(x3 - 5x2 + 6x)/(-x3 - x2 + 12x)
Find: x-intercept(s), y-intercept, hole(s), VA, HA, SA
Then sketch a graph
x-int: (2, 0); y-int: none
holes: (0, 1/2) and (3, 1/7)
VA: x = -4; HA: y = -1; SA: none