Question

Is x³ + 2x² + 3x + 1 reducible over Q? If not, why not? What...

Is x³ + 2x² + 3x + 1 reducible over Q? If not, why not?

What is an irreducible / primitive polynomial?

What does irreducible mean, what is a prime element? Can you give an example for a primitive that is not irreducible or vice versa?

What can you say about the ring R [x]?

Which qualities of rings do you know, can they somehow be ordered (main ideal ring, ZPE, Euclidean)? What do the associated polynomial rings look like?

How can I construct a body for a polynomial P over a field K, which decomposes P into linear factors?

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Q7) Factorise the polynomial f(x) = x3 − 2x2 + 2x − 1 into irreducible polynomials...
Q7) Factorise the polynomial f(x) = x3 − 2x2 + 2x − 1 into irreducible polynomials in Z5[x], i.e. represent f(x) as a product of irreducible polynomials in Z5[x]. Demonstrate that the polynomials you obtained are irreducible. I think i manged to factorise this polynomial. I found a factor to be 1 so i divided the polynomial by (x-1) as its a linear factor. So i get the form (x3 − 2x2 + 2x − 1) = (x2-x+1)*(x-1) which is...
problem 2 In the polynomial ring Z[x], let I = {a0 + a1x + ... +...
problem 2 In the polynomial ring Z[x], let I = {a0 + a1x + ... + anx^n: ai in Z[x],a0 = 5n}, that is, the set of all polynomials where the constant coefficient is a multiple of 5. You can assume that I is an ideal of Z[x]. a. What is the simplest form of an element in the quotient ring z[x] / I? b. Explicitly give the elements in Z[x] / I. c. Prove that I is not a...
True or False, explain: 1. Any polynomial f in Q[x] with deg(f)=3 and no roots in...
True or False, explain: 1. Any polynomial f in Q[x] with deg(f)=3 and no roots in Q is irreducible. 2. Any polynomial f in Q[x] with deg(f)-4 and no roots in Q is irreducible. 3. Zx40 is isomorphic to Zx5 x Zx8 4. If G is a finite group and H<G, then [G:H] = |G||H| 5. If [G:H]=2, then H is normal in G. 6. If G is a finite group and G<S28, then there is a subgroup of G...
Part I If P(x) = 2x 4 - x 2 + 3x - 1, use synthetic...
Part I If P(x) = 2x 4 - x 2 + 3x - 1, use synthetic division to find P (2). A. 17 B. 21 C. 33 Solve x 4 - 11x 2 + 18 = 0. A. {±2, ±9} B. {±√2, ±3} C. {±2,± √3} Part II If P(x) = x 5 + 1 is divided by x + 1, find the remainder. A. -1 B. 0 C. 2 A soccer ball is kicked from the ground in an...
5. Part I If f(x) = 2x 2 - 3x + 1, find f(3) - f(2)....
5. Part I If f(x) = 2x 2 - 3x + 1, find f(3) - f(2). A. 0 B. 7 C. 17 Part II If G( x ) = 5 x - 2, find G-1(x). A. -5x + 2 B. (x + 2)/5 C. (x/5) + 2 Please help me solve this problem and if you can please also show or explain how you got that answer. Thank you! :)
1.) P(2, 4) lies on the graph of y=x4-2x-4 Q is the point (x, x4-2x-4) Write...
1.) P(2, 4) lies on the graph of y=x4-2x-4 Q is the point (x, x4-2x-4) Write an equation for the slope of the secant line through P and Q as a function of x. 2.) Using the formula above, find the slopes fo 1.9, 1.99, 1.999, 2.001, 2.01, and 2.1 (round 4 decimal places) 3.) What is the slope of the tangent line to the curve y=x4-2x-4 at P(2, 4) Can you please explain in detail how to get the...
let p1(x) = x^2-3x-10 ,p2(x)=x^2-5x+1,p3(x)=x^2+2x+3 and p4(x)=x+5 a- As an alternative ; we can form additional...
let p1(x) = x^2-3x-10 ,p2(x)=x^2-5x+1,p3(x)=x^2+2x+3 and p4(x)=x+5 a- As an alternative ; we can form additional equation involving a1,a2,a3,and a4 using differntiation.explain how how to produce a system of equation with unknown constant a1,a2,a3,a4. Since there are 4 unknown ,you will need 4 equattion find them b- Find Basis for the vector space spanned by p1(X),p2(x),p3(x),p4(x). express any reductant vector in terms of linear combination of the others .Note you might want to use row in the changes?
a) What is the average value of f(x) = √ 1 − x^2 over the interval...
a) What is the average value of f(x) = √ 1 − x^2 over the interval 0 ≤ x ≤ 1? (b) How can you tell whether this average value is more or less than 0.5 without doing any calculations?
1. If x+y = 6 and 2x+8y = 9, then what is x? 2. A distant...
1. If x+y = 6 and 2x+8y = 9, then what is x? 2. A distant object reverses its direction from +21.3 km/h to -20.5 km/h over 2.34 years. Find its average acceleration in m/s2 during this interval. 3. An ant has the following initial coordinates xintial = -5.0m, yinitial = 8.0m. If the ant relocates to the coordinates xfinal = 3.0m, yfinal = 0.0m in 24 seconds, what is the magnitude of its displacement? 4. Find the minimum coefficient...
1. Suppose the market demand for Paradise Bakery's cookies is given by the equation P=45-(1/2)Q. What...
1. Suppose the market demand for Paradise Bakery's cookies is given by the equation P=45-(1/2)Q. What quantity sold would maximize the revenue from the cookies? 1-) 40 2- )45 3-) 50 4-) 55 5-) None of these are correct. 2. A monopolist enjoys a monopoly over the right to sell automobiles on a certain island. It imports automobiles from abroad at a cost of $10,000 each and sells them at the price that maximizes profits. One day, the island’s government...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT