1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lapatulllka [165]
3 years ago
8

Give an example of each of the following or explain why no such example exists. (a) Two polynomials of degree 1 in Z4x whose pro

duct is a polynomial of degree 1. (b) Two polynomials of degree 3 in R[x] whose sum is a polynomial of degree 1. (c) Two polynomials of degree 2 in Z6x whose product is a polynomial of degree 5.
Mathematics
1 answer:
andre [41]3 years ago
3 0

Answer:

Step-by-step explanation:

(a)

let, f(x) = 2x+1 & g(x) = 2x+2

So, f(x).g(x) = (2x+1).(2x+2) = 4x² + 6x + 2 = 2x+2 in Z_4[x]

So, product of two 1 degree polynomials is a 1-degree polynomial in Z_4[x]

(b)

let, f(x) = 2x³ - 3x² + 5x + 7 & g(x) = -2x³ + 3x² + x + 3 be two polynomials in R[x]

So, f(x) + g(x) = 6x + 10, which is a polynomial of degree 1 in R[x]

(c)

this is not possible, since, if f & g are 2 polynomials in any polynomial ring S, then, we always have,

deg(f.g) <= deg(f) + deg(g)

So, deg(f.g) = 5 (as desired) but, deg(f) + deg(g) = 2+2 = 4 but, 4 < 5

So, this is not possible.

So, no such example exists.

You might be interested in
Rewrite in simplest terms: 2(-4p-6)-5p2(−4p−6)−5p
irina1246 [14]

Answer: 20p³+30p²-13p-12

Step-by-step explanation:

2(-4p-6)-5p²(-4p-6)-5p

-8p-12+20p³+30p²-5p

20p³+30p²-13p-12

please click thanks and mark brainliest if you like :)

3 0
3 years ago
Read 2 more answers
Mrs. Wilson packed supply bags for her students to use in a science experiment. In each bag she put 3 rubber bands and 4 paper c
n200080 [17]

Answer:

64

Step-by-step explanation:

In each supply bag, Mrs. Wilson packed 3 rubber bands and 4 paper clips for her students.

Now, it is given that she had used 48 rubber bands.

Hence, there will be (48/3) =16 supply bags that had been used.

Now, in 16 supply bags, there will be (16×4) =64 paper clips.

Therefore, 64 paper clips that she had used. (Answer)

3 0
2 years ago
There are 40 girls and 60 boys in the math club the coach wants to divide the entire club into teams where each team has the sam
lapo4ka [179]
40 and 60
40 = 20 x 2
60 = 20 x 3

GCF = 20

<span>the greatest number of teams coach can make is 20
each team can have 2 girls and 3 boys</span>
6 0
3 years ago
Margaret bought 40 ounces of bananas for $5.00. How much did Robert pay for 12 ounces?
Brrunno [24]
It’s 57.23 dhe paided for
3 0
2 years ago
Read 2 more answers
I’m confused on this one
Alenkinab [10]

Remark

I would have had the answer a whole lot sooner if I would have read the question properly. The figure in the circle is called a cyclic quadrilateral. It has the odd property that the angles that are opposite each other add up to 180o.

So DEB + DCB = 180o

DEB = 180 - 87

DEB = 93o

Note: The arcs marked 60 and 76 have nothing whatever to do with this problem.

7 0
2 years ago
Other questions:
  • [-x - 2y = 7<br> [3x + y = 6
    13·1 answer
  • AB Is perpendicular to line segment
    13·1 answer
  • How do you convert 3/1/4 to fractional notation
    14·1 answer
  • -2c = -18<br><br> a. c= -9<br> b. c= -36<br> c. c= 9<br> d. c= 36
    11·2 answers
  • It took Jen, who biked at a speed of 12 mph, 20 minutes to get home. What is Jim’s speed, if it took him only 15 minutes to bike
    5·1 answer
  • HELP!!! WILL GIVE BRAINLIEST!!!! 40 POINTS!!!!!! The agriculture department of a university works with individuals wanting to bu
    11·1 answer
  • Select the correct answer. What is the factored form of 24y5 + 3y2?<br><br>​
    9·1 answer
  • Can someone slove that
    5·1 answer
  • A ball is launched out of a cannon that is 24 feet off the ground. The height of the ball after "t" seconds is represented by
    14·1 answer
  • What is the missing fifth term in the<br> pattern below?<br> 1,8, 27, 64, ___
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!