Question
In: Advanced Math
Determine whether the polynomial is reducible or irreducible in the given polynomial ring. Justify your answers....
Determine whether the polynomial is reducible or irreducible in the given polynomial ring. Justify your answers.
(c) x^4 + 1 in Z5[x]
(e) 2x^3 − 5x^2 + 6x − 2 in Z[x]
(f) x^4 + 4x^3 + 6x^2 + 2x + 1 in Z[x]. Hint: Substitute x − 1 for x.
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Factor the following polynomials as a product of irreducible in the given polynomial ring. A. p(x)=2x^2+3x-2...
Factor the following polynomials as a product of irreducible in
the given polynomial ring.
A. p(x)=2x^2+3x-2 in Q[x]
B. p(x)=x^4-9 in Q[x]
C. p(x)=x^4-9in R[x]
D. p(x)=x^4-9in C[x]
E. f(x)=x^2+x+1 in R[x]
F. f(x)=x^2+x+1in C[x]
Determine whether the polynomial f(x) is irreducible over the indicated field. (a) f(x) = 4x^ 3...
Determine whether the polynomial f(x) is irreducible over the
indicated field. (a) f(x) = 4x^ 3 + 10x^2 + 16x − 11 over Q (b)
f(x) = 7x^ 4 − 9x^ 2 + 6 over Q (c) f(x) = x^3 − x + 1 over Q (d)
f(x) = x ^4 + 2x ^2 + 2 over Q (e) f(x) = x^ 4 + 2x^ 2 + 2 over C
(f) f(x) = x ^4 + 2x^ 2 + 2...
Determine whether the following statements are true or false , and justify your answer 1- Given...
Determine whether the following statements are true or false , and
justify your answer
1- Given that accounting information is a public good , we
have to have mandatory accounting regulation.
2- It is better to lobby the accounting standard - setter
indirectly rather than directly.
3- A change in reported income is an economic consequence of a
change in an accounting standard's requirements
PLEASE JUSTIFY EVEN IF YES
Determine whether each of the following statements is TRUE or FALSE. Justify all the answers in...
Determine whether each of the following statements is TRUE or
FALSE. Justify all the answers in few sentences.
1. In the Ricardian model with 2 goods (Wine and Cheese) and 2
countries (Home and Foreign) and (except otherwise noted) identical
preferences between countries:
(a) If both countries have the same number of workers and Home
has absolute advantages in both goods then Home must have a higher
wage.
(b) The Home country is never made worse off by productivity
growth...
Determine whether each of the following statements is TRUE or FALSE. Justify all the answers in...
Determine whether each of the following statements is TRUE or
FALSE. Justify all the answers in few sentences.
1. In the Ricardian model with 2 goods (Wine and Cheese) and 2
countries (Home and Foreign) and (except otherwise noted) identical
preferences between countries:
(a) If both countries have the same number of workers and Home
has absolute advantages in both goods then Home must have a higher
wage.
(b) The Home country is never made worse off by productivity
growth...
1.Determine whether S spans V . Justify your answers. V = C ^0 [−1, 1] (the...
1.Determine whether S spans V . Justify your answers.
V = C ^0 [−1, 1] (the vector space of continuous functions on
[−1, 1]) and S = {1, t, t2 , t3 , . . . }.
2.Let S be a set in a vector space V and v any vector. Prove
that span(S) = span(S ∪ {v}) if and only if v ∈ span(S).
Determine whether each system is LTI, causal and/or stable and with or without memory. Justify answers....
Determine whether each system is LTI, causal and/or stable and
with or without memory. Justify answers.
a) y[n + 1] + 4y[n] = 3x[n + 1] - x[n]
b) y[n] = nx[2n]
Determine whether each system is LTI, causal and/or stable and with or without memory. Justify answers....
Determine whether each system is LTI, causal and/or stable and
with or without memory. Justify answers.
a) y(t) =sen(x(t))
b) y(t) = dx/dt + x(t)
For each of the following statements, determine whether it is true or false and justify your...
For each of the following statements, determine whether it is
true or false and justify your answer. a. Every function f : [0, 1]
~ lR has a maximum. b. Every continuous function f :[a, b] ~ lR has
a minimum. c. Every continuous function f : (0, 1) ~ lR has a
maximum. d. Every continuous function f : (0, 1) ~ lR has a bounded
image. e. If the image of the continuous function f: (0, 1) ~...
For each of the following statements, determine whether it is true or false and justify your...
For each of the following statements, determine whether it is
true or false and justify your answer.
a. If the function f + g: IR --> IR is continuous, then the
functions f :IR --> IR and g :IR --> IR also are
continuous.
b. If the function f^2 : IR --> R is continuous, then so is the
function f :R --> IR.
c. If the functions f + g: IR and g: IR --> IR are continuous,
then...
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