Traits of Polynomials
Polynomial Factors
Polynomial Arithmetic
Rational Functions
Random Trivia
100
What is the degree of the polynomial? Is it odd or even?
3x^2 + x - 4x^4 + 5x^7
7, odd
100
What do zeros of a function mean?
Zero's mean that the x-values make the expression =0
The x-values where the function touches the x-axis
100
Simplify (4 - x - 2x2) - (-2 + 3x - x3)
x3 - 2x2 - 4x + 6
100
Find the vertical asymptote(s)
f(x)=(x-5)/(x-7)
x=7
100
Fill in the blank: Never divide by ______.
Zero! Division by zero creates an asymptote
200
Show us with your arms what a negative, odd end behavior would look like!
Up, down!
200
Is (3x + 1) a factor of 9x2 + 3x?
Yes! Division-Remainder is 0, Factoring-GCF
200
Simplify (x+1)(x3+2x2+3x-8)
x4+3x3+5x2-5x-8
200
Find the vertical asymptote of the function
f(x) = x/(3x - 6)
x=2
200
Mistakes Allow _____ to Happen!
Mistakes Allow Thinking to Happen!
300
x -> -oo, y -> -oo
x -> +oo, y -> +oo
What is the degree (even or odd) and sign of the leading coefficient of the graph (positive or negative) shown in the end behavior above?
odd, positive
300
Is it possible to have a polynomial that has an odd degree, rises to the left and falls to the right, and three factors that all have a multiplicity of 2?
No
300
The value of P(0) for this polynomial.
P(x)=x^3-x^2+3x-2
-2
300
What is the
*Vertical Asymptote
*Horizontal Asymptote
Vertical Asymptote x=2
Horizontal Asymptote y= 0.5
300
What letter doesn’t appear in any U.S. state name?
Q
400
What is the leading term of the following polynomial:
-2(2x+3)^ 3( -x+1)^2(x+3)^3
-16x^8
400
State a possible equation for this graph (you do not need to find the leading coefficient, just the factors from the roots):
(-1/144)((x+4)(x+3)(x+1)(x-3)(x-4)) or
((x+4)(x+3)(x+1)(x-3)(x-4))-145
400
The quotient of these polynomials, using long division.
(x^3-64)/(x^2+4x+16)
x - 4
400
Given
y=(12x-2)/(2x)
What is the
*Vertical Asymptote
*Horizontal Asymptote
*Vertical Asymptote x = 0
*Horizontal Asymptote y = 6
400
What occurs once in a minute, twice in a moment, but never in a thousand years?
The letter M
500
(ax - 1)(bx + 2) = cx2 - x - 2 for all values of x, and a + b = 10, what is the value of c?
c = 21
(a = 3, b = 7)
500
Write the polynomial in factored form:
2x3 + 14x2 + 20x
State the x-intercepts, their multiplicities, and the y-intercept
2x(x + 5)(x + 2)
x-int:
x = 0, m = 1, cross
x = -5, m = 1, cross
x = -2, m = 1, cross
y-int:
y = 0
500
(x3 + 11x + 12) ÷ (x + 3)
x2 - 3x + 20 - 48/(x+3)
500
What is the end behavior of this function:
(3x-17)/((x+8)(x-8)
Horizontal asymptote at y = 0.
500
The best school in the world is ____
Walnut Hill!