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Level 527

Higher Degree Polynomials


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polynomial graph
continuous (can be drawn without lifting pencil)
End Behavior
Look at HA
Multiplicity
The number of times the related linear factor is repeated in the factored form of the polynomial.
sum of cubes
An expression of the form a^3 +b^3. It can be factored as (a + b) (a^2 - ab + b^2).
differences of cubes
(a^3-b^3) = (a^2 + ab + b^2)
Rational Root Theorem
lists all possible rational roots (p/q)
Factor Theorem
A polynomial f(x) has a factor (x-c) if and only if f(x) = 0
Local Max
Value of a function or a graph that is greater than all nearby points
Local Min
A value of a function or a graph that is less than all nearby points
Extreme Values
Max and min collectively
up and up
When a is positive and even?
down and down
When a is negative and even?
down and up
When a is positive and odd?
up and down
When a is negative and odd?
Maximum number of zeros?
value of first exponent
Maximum number of turns?
value of first exponent minus one
Even
An integer n is defined to be even if n=2k for some integer k.
Odd
An integer n is defined to be odd if n=2k+1 for some integer k.
Division Algorithm
f(x)/d(x)=q(x)+r(x)/d(x) or f(x)=d(x)q(x)+r(x)
Remainder Theorem
If a polynomial f(x) is divided by (x-c), the remainder is f(c)