Algebra 2 Unit 5 Flashcards
What is a monomial?
A monomial is a number, variable, or a product of numbers and variables
The Exponent Product Rule means to ______ the exponents on the same base
Add
The Exponent Power Rule means to ______ the exponents on the same base
Multiply
The Exponent Quotient Rule means to ______ the exponents on the same base
Subtract
The Zero Exponent Rule means that any base to the zero power is …
1
The Negative Exponent Rule means that any base with a negative exponent must be …
Moved to the opposite numerator/denominator from where it was and the expanent made positive
When adding or subtracting monomials, make sure you …
Combine Like Terms!
How do you write Polynomials in Standard form?
Write them in Alphabetical and Descending order
What do you call the highest exponent of a polynomial?
It is called the degree
What is the definition of a polynomial?
It is the sum or difference of many monomials
What do you call a polynimial with a degree of 0?
A constant
What do you call a polynimial with a degree of 1?
Linear
What do you call a polynimial with a degree of 2?
Quadratic
What do you call a polynimial with a degree of 3?
Cubic
What do you call a polynimial with a degree of 4?
Quartic
What do you call a polynimial with a degree of 5?
Quintic
What do you call a polynimial with only one term?
A monomial
What do you call a polynimial with only two terms?
A binomial
What do you call a polynimial with only three terms?
A trinomial
What do you call a polynimial with four or more terms?
A Polynomial
What does the Constant Polynomial Parent Function look like?
What does the Linear Polynomial Parent Function look like?
What does the Quadratic Polynomial Parent Function look like?
What does the Cubic Polynomial Parent Function look like?
What does the Quartic Polynomial Parent Function look like?
What does the Quintic Polynomial Parent Function look like?
Describe the end behavior or a function with a POSITIVE leading coefficient and an EVEN degree
As x goes to negative, y goes to positive As x goes to positive, y goes to positive
Describe the end behavior or a function with a POSITIVE leading coefficient and an ODD degree
As x goes to negative, y goes to negative As x goes to positive, y goes to positive
Describe the end behavior or a function with a NEGATIVE leading coefficient and an EVEN degree
As x goes to negative, y goes to negative As x goes to positive, y goes to negative
Describe the end behavior or a function with a NEGATIVE leading coefficient and an ODD degree
As x goes to negative, y goes to positive As x goes to positive, y goes to negative
What is a turning point?
The point(s) at which a polynomial function switched direction
What do we call a turning point that is higher than any nearby point?
A relative maximum
What do we call a turning point that is lower than any nearby point?
A relative minimum
What are Maximum and Minimum values called?
Extrema
What do turning points define in a function / on a graph?
Where the function is increasing or decreasing
What are zeros?
The point(s) at which the function intersects the x-axis
A polynomial can only have how many real zeros/solutions?
The highest it can have is the degree value of the function
What does factoring a polynomial do?
It reveals it’s linear factors to be solve for possible solutions
What is a multiplicity?
The highest degree each individual linear factor has
What does a function do at it’s zero when it has an ODD multiplicity?
It Intersects/Crosses the x-intercept or zero
What does a function do at it’s zero when it has an EVEN multiplicity?
It bounce back up off of the x-intercept or zero
When you are given the difference of two terms being squared, what can you suspect?
The difference of squares is in play
When you are given the sum of two terms being cubed, what can you suspect?
The sum of cubes is in play
When you are given the difference of two terms being cubed, what can you suspect?
The differene of cubes is in play
When you have a trinomial, what are your options?
Factor or use the Quadratic Formula
When you are given 4 terms that cannot be combined, what should you suspect?
Factor by Grouping
What is the Difference of Squares Formula?
What is the Difference of Cubes Formula?
What is the Sum of Cubes Formula?
