Polynomial Basics
What is the degree of the polynomial:
3x^4-2x^3+x-5
4
Multiply
(x+3)(x-2)
x^2+x-6
What is the end behavior of x^3-2x ?
-∞ to ∞
What is the remainder when
x^2+3x+5 is divided by (x-2) ?
15
What polynomial represents the volume of an open-top box made from a piece of square paper with side length s and cutting out squares of side length x from each corner?
V=x(s-2x)(s-2x)
Which country is known as the "Land of the Rising Sun"?
Japan
What is the leading coefficient of
7x^5-4x+2
7
Divide:
(x^2+4x+3)÷(x+1)
x+3
What is the end behavior of
-x^4+2x^3-x
-∞ -∞
According to the Polynomial Remainder Theorem, what does f(a) represent when dividing f(x) by x−a?
The remainder
A 10-inch by 8-inch sheet of metal has squares of side x cut from each corner to form an open box. Write a polynomial for the volume.
V=x(10-2x)(8-2x)
What is the longest river in the world?
The Nile
What does it mean for a polynomial to be in standard form?
Terms are written in descending order of exponent value
Factor completely
x(x-3)(x+3)
x(x-3)(x+3)
How does the graph behave when a factor has an even multiplicity?
It touches the x-axis but does not cross it.
Use the remainder theorem to find the remainder when f(x)=x^3-4x+6 is divided by x+2 .
6
What is the degree of the polynomial representing the volume of an open-top box created from a 12-inch square?
3
What is the capital of Canada?
Ottawa
Identify the constant term in
6x^3-2x+9
What is the quotient when
x^4-16 divided by (x-2)
x^3+5x^2+7x-5
How does multiplicity effect your drawing of a polynomial's graph?
determins whether we cross the x-axis at a zero or not
Find the remainder when x^3+2x^2-x+4 is divided by x-3
46
A rectangular sheet of dimensions 12 by 9 inches has squares of side x cut from each corner. Write a polynomial function for the volume.
V=(12-2x)(9-2x)x
Which continent is home to the Sahara Desert?
Africa
Write the polynomial in standard form
4x^2-5+x^3
x^3+4x^2-5
Multiply
(2x-1)(x^2+3x+5)
2x^3 +5x^2+7x-5
Give an example of a polynomial that has an odd degree and a negative leading coefficient.
ie.
-x^3+2x^2-3x+7
If f(1)=0 what does that tell us about the polynomial?
(x-1)
is a factor of the polynomial
If a polynomial function represents the volume of an open-top box created by a piece of paper, what key feature of its graph helps determine the maximum volume?
The relative max of the function between 0 and half the shortest length of the paper.
Which country has the most pyramids in the world?
Sudan