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Example Questions
Example Question #1 : Fields
What definition does the following correlate to?
If is a prime, then the following polynomial is irreducible over the field of rational numbers.
Primitive Field Theorem
Ideals Theorem
Principal Ideal Domain
Gauss's Lemma
Eisenstein's Irreducibility Criterion
Eisenstein's Irreducibility Criterion
The Eisenstein's Irreducibility Criterion is the theorem for which the given statement is a corollary to.
The Eisenstein's Irreducibility Criterion is as follows.
is a polynomial with coefficients that are integers. If there is a prime number that satisfy the following,
Then over the field of rational numbers is said to be irreducible.
Example Question #2 : Fields
Identify the following definition.
For some subfield of , in the Euclidean plane , the set of all points that belong to that said subfield is called the __________.
Angle
None of the answers.
Plane
Constructible Line
Line
Plane
By definition, when is a subfield of , in the Euclidean plane , the set of all points that belong to is called the plane of .
Example Question #1 : Geometric Fields
Identify the following definition.
Given that lives in the Euclidean plane . Elements , , and in the subfield that form a straight line who's equation form is , is known as a__________.
Circle in
Line in
Plane
Angle
Subfield
Line in
By definition, given that lives in the Euclidean plane . When elements , , and in the subfield , form a straight line who's equation form is , is known as a line in .
Example Question #3 : Fields
Identify the following definition.
Given that lives in the Euclidean plane . Elements , , and in the subfield that form a straight line who's equation form is , is known as a__________.
Line in
Subfield
Plane
Circle in
Angle
Line in
By definition, given that lives in the Euclidean plane . When elements , , and in the subfield , form a straight line who's equation form is , is known as a line in .
Example Question #4 : Fields
Identify the following definition.
If a line segment has length and is constructed using a straightedge and compass, then the real number is a __________.
Magnitude
Constructible Number
Plane
Angle
Straight Line
Constructible Number
By definition if a line segment has length and it is constructed using a straightedge and compass then the real number is a known as a constructible number.
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