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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)