Term
If p/q is a rational zero of P(x), then what doe p/q equal?
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Definition
((Possible factors of asubscrpt0)/(Possible factors of asubscrptn))
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Term
What are the potential zeroes of a polynomial function?
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Definition
Factors of the Constant Term Divided By Constants of the Leading Coefficient
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Term
How do you find out if a possible zero is actually a rational zero?
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Definition
Complete synthetic division and if you get zero as a remainder, it is a rational zero.
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Term
How do you find all the roots for the function f(x)=0?
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Definition
1.) Factor out
(x(Opposite Sign of rational zero)rational zero)
[This is easily done by using synthetic division with the rational zero]
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2.)Now use the quadratic formula to find the roots of f(x)=0. [Unless it still hasn't formed a quadratic function meaning you must test another rational zero using synthetic division, except you now apply it to the new function, then using quadratic formula find the roots of f(x)=0.]
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3.)Your solution set: (rational zeroes, the roots of (fx)=0)
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Term
How do you find the number of positive real roots?
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Definition
Number of sign changes in f(x) or that number subtracted by an even integer.
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Term
How do you find the number of negative real roots?
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Definition
Number of sign changes in f(-x) or that number subtracted by an even integer.
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Term
If the degree of a polynomial is greater than or equal to one, how many not necessarily distinct zeroes are there?
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Definition
Equal to that of the degree
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Term
If a polynomial needs another zero, and one of its zeroes is a+bi, then what must the other zero be, based on the conjugate pairs theorem?
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Definition
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Term
How do you find a polynomial P(x) with real coefficient having a degree "A", leading coefficient "B", and zeros "C", 0 (multiplicity 3), D-Ei?
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Definition
(Bx^3)(x-C)[((x-D)^2)+(E^2)]
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