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31 Cards in this Set

  • Front
  • Back

What does the degree of an equation tell you?

The maximum number of possible roots

What does descartes rule of signs tell you?

The number of imaginary, negative and positive roots there are

Using descartes, how do you find the maximum number of positive roots?

Write the polynomial in desc order


Count how many times the sign changes

Using descartes how do you find the maximum number of negative roots?

find f(-x)


Count how many times the sign changes

Using descartes how do you find the highest number of complex roots?

The highest degree in the equation

How do you calculate a list of all possible roots for a polynomial using the rational root theorem?

Take all possible factors of the constant term and divide by all possible factors of the leading coefficient.

How do you test the roots generated by the rational root theorem?

Long divide the quadratic by x - [root]


If the remainder is 0 then the root is an actual solution

When can you use synthetic division instead of long division?

When dividing by a first degree binomial with a leading coefficient of 1

What are the steps in synthetic division?

Order the coefficients and the constant filling in missing entries with 0


Drop down the first coefficient and multiple it by the root


Put the calculated value under the next coefficient and add them


Multiple the value by the root and put it under the next coefficient


Continue process for all coefficients

When using synthetic division, how do you know a test root is an actual root?

If the value under the last coefficient is 0

How do you test for a double root if the test root is an actual root?

Divide the solution of the first division

What does the remainder theorem say about the remainder when dividing a quadratic?

The the remainder is the value of the quadratic when you plug the root into the equation.

What can be said about the graph of a polynomial when the leading coefficient is positive and the degree of the polynomial is even?

Both ends of the graph point up

What can be said about the graph of a polynomial when the leading coefficient is negative and the degree of the polynomial is even?

Both ends of the graph point down

What can be said about the graph of a polynomial when the leading coefficient is positive and the degree is odd?

The left side of the graph points down and the right side of the graph points up

What can be said about the graph of a polynomial when the leading coefficient is negative and the degree is odd?

The left side of the graph points up and the right side of the graph points down

What property states:


a = a

Reflexive property

What property states:


if a = b, then b = a

Symmetric property

What property states:


if a = b and b = c, then a = c

Transitive property

What property states:


a + b = b + a

Commutative property of addition

What property states:


a * b = b * a

Commutative property of multiplication

What property states:


(a + b) + c = a + (b + c)

Associative property of addition

What property states:


(a * b) * c = a * (b * c)

Associative property of multiplication

What property states:


a + 0 = a

Additive Identity property

What property states:


a * 1 = a

Multiplication identity

What property states:


a + (-a) = 0

Additive inverse property

What property states:


a * (1/a) = 1

Multiplication inverse property

What property states:


a(b + c) = a * b + a * c

Distributed property

What property states:


a * 0 = 0

Multiplicative property of zero

What property states:


a * b = 0 then a = 0 or b = 0

Zero-product property

What is a one to one function?

A function were there is a unique output for every input