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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 |
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What does descartes rule of signs tell you? |
The number of imaginary, negative and positive roots there are |
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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 |
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Using descartes how do you find the maximum number of negative roots? |
find f(-x) Count how many times the sign changes |
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Using descartes how do you find the highest number of complex roots? |
The highest degree in the equation |
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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. |
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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 |
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When can you use synthetic division instead of long division? |
When dividing by a first degree binomial with a leading coefficient of 1 |
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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 |
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When using synthetic division, how do you know a test root is an actual root? |
If the value under the last coefficient is 0 |
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How do you test for a double root if the test root is an actual root? |
Divide the solution of the first division |
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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. |
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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 |
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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 |
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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 |
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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 |
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What property states: a = a |
Reflexive property |
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What property states: if a = b, then b = a |
Symmetric property |
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What property states: if a = b and b = c, then a = c |
Transitive property |
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What property states: a + b = b + a |
Commutative property of addition |
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What property states: a * b = b * a |
Commutative property of multiplication |
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What property states: (a + b) + c = a + (b + c) |
Associative property of addition |
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What property states: (a * b) * c = a * (b * c) |
Associative property of multiplication |
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What property states: a + 0 = a |
Additive Identity property |
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What property states: a * 1 = a |
Multiplication identity |
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What property states: a + (-a) = 0 |
Additive inverse property |
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What property states: a * (1/a) = 1 |
Multiplication inverse property |
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What property states: a(b + c) = a * b + a * c |
Distributed property |
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What property states: a * 0 = 0 |
Multiplicative property of zero |
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What property states: a * b = 0 then a = 0 or b = 0 |
Zero-product property |
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What is a one to one function? |
A function were there is a unique output for every input |