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[3.1]Exponents are used to…
Denote repeated multiplication
[3.1]Example of exponents
[3.1]Powers of -1
Exponent of 1
Consider positive powers of 2…
Negative Exponents
Power of Product Rule
Product rule
Quotient Rule
Power rule
Simplifying with exponents
[3.2] Factors
Real numbers, variables, or expressions multipled ( or divided ) together
[3.2] Terms
Real numbers, variables or expressions added/subtracted Together
[3.2] Coefficient
The value multipled to a variable
[3.2] Degree
The exponent of the variable
Like Term
Terms that share the same variables and variable exponents
Add/subtract like Terms by adding /subtracting their…
Coefficients
Polynomials
expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s)
Poly = Many
Nomials = Terms
Polynomials Standard Forms
Degree of a Polynomial
The largest degree of the variables (aka :n)
Distributive Property
[3.2] Special cases of distributive property
Perfect Square Trinomial
Negative
Positive
Difference if Squares
[3.2] Polynomial operations
Replace the function notation with the function definition.
[3.2] Factoring
Is the process of undoing distribution ( turning sums into products of sums )
There are two types!
Expanded forms
Factored forms
[3.2] Process of Factoring
We need to find A and B we will use “restricted guess and check”
Guessing and checking values within certain parameter
[3.2]What if the coefficient of 𝒙𝟐 is not 1?
[3.2] GCD !
Greatest common Divisor of two terms is the largest factor shared between both terms
Only do this is possible
[3.2] What If factorization is possible?
If a polynomial cannot be factored it is considered to be prime
[3.2] Factoring by grouping!
If you rewrite the polynomial, you may be able to factor out the GCD.
[3.2] ABC method!
[3.2] Example of ABC method
[3.2] Special factoring techniques: Perfect Square Trinonial
[3.2] Special Factoring :Different of squares
[4.1] a quadratic function has the general form…
[4.1]The graph of quadratic function are called..
Parabolas
[4.1] quadratic function graphs look like
[4.1] Quad-Ratic
Largest term is Square. Square has 4 sides ( reminder )
[4.1] properties of Parabolas
Vertex, vertical and horizontal intercept and Concavity.
[4.1] Vertex
Its the point whose y-value is either less than or greater than the y - values of all the other points
The lowest or the highest
[4.1] if the parabola opens UP ( U shape ) then it is…(concavity)
Concave Up
[4.1] ( Concavity ) if the parabola opens down then it is is..…
Concave down
[4.1] Vertical intercept…
Parabolas will always have just 1 vertical intercept
[4.1] horizontal intercept ….
Parabola may have… 0 1 or 2 horizontal intercepts
[4.1] how to know if something is a quadratic function…
Knowing if the quadratic function is up or down but If it isn't either then it isn't one
[4.1]Another example of quadratic functions
[4.1] Zero Factors
If a product equals zero then at least the factor must be Zero
If ab=0 then A= 0 and/or b= 0
[4.1] the horizontal interception(s) of a quadratic fiction occurs when…
[4.1] the horizontal interceptions for solving quadratic equations are also called..…
“Zeroes” and “roots” of the polynomial
[4.1] Word problem for solving quadratic equations
[4.1]Square Root
[4.1] getting two values from the same operations is not ideal so….
[4.1] Square Root Property
[4.1] Solving for variable inside bases
[4.1] Perfect Square Trinomials
[4.1] Completing the Square