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Example Questions
Example Question #1 : Splitting Fields
What definition does the following correlate to?
If
is a prime, then the following polynomial is irreducible over the field of rational numbers.
Gauss's Lemma
Ideals Theorem
Principal Ideal Domain
Primitive Field Theorem
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 #1 : Geometric 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 theAngle
Line
Constructible Line
None of the answers.
Plane
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 #2 : 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 aCircle in
Subfield
Angle
Plane
Line in
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 : 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 aLine in
Subfield
Angle
Circle in
Plane
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 #1 : Fields
Identify the following definition.
If a line segment has length __________.
and is constructed using a straightedge and compass, then the real number is aConstructible Number
Angle
Plane
Magnitude
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.Certified Tutor
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