Definitions
The highest exponent occuring on x of a polynomial in x is called the ___________ of the polynomial
degree
True or False: The degree of -2x^3+10x is even.
False
What is the equation for the volume of an open top box made by cutting squares of length x out of the corners of an 8x10 sheet of cardstock?
V(x)=
V(x)=x(8-2x)(10-2x)
What are the zeros of 5x(2x-3)(x+7) ?
0, 3/2 , -7
What is the vertical intercept of
p(x)=(2x-1)(4x+3)(x+7) ?
-21
Random Trivia!!
A lemniscate is a shape that indicates what concept in mathematics?
Infinity
oo
As x goes to positive infinity, what happens to f(x)=-2x^3+10x ?
It goes to negative infinity.
Random Trivia!!
Which U.S. Senator is RuPaul's distant cousin?
Senator Cory Booker
Either (x+6) or (x-6) is a factor of g(x)=x^3-4x^2-27x+90
Which one is it?
(x-6)
At what points does the graph of f(x)=(x-3)(x-9) intersect the graph of g(x)=x-9 ?
(9,0) and (4,-5)
The power to which a factor occurs in the factored form of a polynomial is its ________________.
multiplicity
What is the constant term of f(x)= -2x^3+10x ?
0
An open top box is made by cutting squares of length x out of the corners of an 10x12 sheet of cardstock. What is a reasonable domain for x?
Random Trivia!!
What is Arachibutyrophobia?
The fear of peanut butter sticking to the roof of your mouth
In the graph of f(x)=(5x-3)(x+2)^2(x+7) a relative minimum will occur between which two zeros?
-2 and 3/5
The ___________ ___________ states that given any (x - a) and polynomial p(x), p(x) divided by (x - a) has remainder p(a).
Random Trivia!!!
What is a group of bats called?
a cauldron
The equation for the volume of an open top box made by cutting squares of length x inches out of the corners of a sheet of cardstock is V(x)=x(5-2x)(6-2x)
If we want the volume of the box to be greater than zero, then the height needs to be strictly less than how many inches?
2.5 inches
(x-3) is a factor of
f(x)=x^3-3x^2-x+3
Write f(x) as a product of linear factors.
f(x)=(x-3)(x-1)(x+1)
Describe the end behavior of
p(x)=(x-3)(4-x)(5-x)
as x->oo , p(x)->oo
as x->-oo , p(x)->-oo
The __________ ______ of a polynomial in x is the term with the highest power of x.
leading term
As x goes to negative infinity, what happens to f(x)= -2x^3+10x ?
It goes to positive infinity.
EXTRA CHALLENGE QUESTION:
A sheet of cardstock will be used to create an open top box of volume: 4x^3-34x^2+72x
If the width of the sheet of cardstock is 8 inches, what is the length?
9 inches
Let h(x)=x^4-11x^3+ux^2-13x-60
If we know that (x+1) is a factor, what is u?
35
Random Trivia!!
What is light amplification by stimulated emission of radiation more commonly know as?
a laser
(LASER = Light Amplification by Stimulated Emission of Radiation)