if f(x) ε F[x] is not irreducible, then F[x]/ contains zero-divisors.
Suppose that f(x) is not irreducible in F[x]. Then we can write f(x) as the product of two non-constant polynomials g(x) and h(x), where the degree of g(x) is less than the degree of f(x) and the degree of h(x) is less than the degree of f(x).
Therefore, in F[x]/(f(x)), we have:
g(x)h(x) ≡ 0 (mod f(x))
This means that g(x)h(x) is a multiple of f(x) in F[x]. In other words, there exists a polynomial q(x) in F[x] such that:
g(x)h(x) = q(x)f(x)
Now, let us consider the images of g(x) and h(x) in F[x]/(f(x)). Let [g(x)] and [h(x)] be the respective images of g(x) and h(x) in F[x]/(f(x)). Then we have:
[g(x)][h(x)] = [g(x)h(x)] = [q(x)f(x)] = [0]
Since [g(x)] and [h(x)] are non-zero elements of F[x]/(f(x)) (since g(x) and h(x) are non-constant polynomials and hence non-zero in F[x]/(f(x))), we have found two non-zero elements ([g(x)] and [h(x)]) in F[x]/(f(x)) whose product is zero. This means that F[x]/(f(x)) contains zero-divisors.
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Which polynomial represents the difference below?
2x +7X+6
(3x? – X
A. - x + 6x + 6
B. 2x2 + 4x + 6
c. 2x2 + 5x + 6
D. - x2 + 3x + 6
Answer:
-x²-8x+6
Step-by-step explanation:
Given the polynomial expression
2x²+7x+ 6 and 3x² – X
Taking their difference
2x²+7x+ 6 - (3x² – X)
2x²-3x²+7x+x+6
-x²-8x+6
Hence the required difference is -x²-8x+6
Answer:
-x²+8x+6
Step-by-step explanation:
Ape-x
I NEED HELP WITH THESE ASAP!
Answer:
I can not see it
Step-by-step explanation:
Convert the decimal below to a fraction in simplest form. 0.689
Answer:
689 / 1000 is the answer
Step-by-step explanation:
zzzzzzzzzzzzz
Figs come in 2.4 lb bags. Apples come in 7.2 lb bags. How many times as many pounds are the apple bags as the fig bags?
Answer:
3 times as many pounds
Step-by-step explanation:
7.2 / 2.4 = 3 times as many pounds
Hope that helps!
what does the ! after a number mean.
explain in your own words and give 5 examples.
Answer: it means that you multiply the number by the numbers counting to 0
Step-by-step explanation:4!=4•3•2•1
Help Please........
Answer:
4
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
(4 x 2)/2 + (4 x (6-2))/2 = 12
Plz help me !!!!!!!!!!
C i think????????????????????? :D
Can somone help please? Thx
Answer:
I would say the answer is 0.69
Step-by-step explanation:Because if you multiply 7 times 0.69 it gives you 4.83
Answer:
The answer is 1.45
Step-by-step explanation:
Divide 7 and 4.83 and the answer is 1.447.
which one pls help me i’ll give extra points
Answer:
C
Step-by-step explanation:
Answer:
A. The doctors will give Charlie an operation
Step-by-step explanation:
Which equations are correct?
Select each correct answer.
−4b3(5b2+3)=−20b6−12b3
−6y4(4y2+2)=−24y8−12y4
−5a4(2a2+4)=−10a6−20a4
−4x2(2x2+5)=−8x4−20x2
A company has 200 employees there are 150 female employees. 40 employees are under the age of 20. The probability of randomly selecting an employee who is female or is under the age of 30 is 85%. What is the probability of randomly selecting an employee who is female and under the age of 30?
Answer and explanation:
Probability= number of favorable outcomes/ total number of outcomes
Probability of selecting an employee who is female= number of female employees/ total number of employees
Probability of selecting an employee who is female= 150/200
Probability of selecting an employee who is under 30= number of employees under 20/ total number of employees
Probability of selecting an employee who is under 30 = 40/200
Probability of randomly selecting an employee who is female and under the age of 30= Probability of selecting an employee who is female × Probability of selecting an employee who is under 30
Probability of randomly selecting an employee who is female and under the age of 30= 150/200×40/200=15/20×4/20=3/20= 0.15
Therefore there's a 15% chance of selecting an employee who is female and under the age of 30
The right triangle below has legs of length and.
The hypotenuse has length.
Four copies of this triangle are arranged as follows.
The hypotenuses form a square of side length and area.
Answer the questions below to find how, and are related.
Part 1: Compute the total combined area of the four triangles:
Part 2: Compute the area of the large (outer) square:
Part 3: Using your answers in Parts 1 and 2, find the area of the small (inner) square.
Part 4: We are given the side lengths and. Compute.
Part 5: Use, or complete the statement below.
Answer + explanation:
Part 1: First, find the area of one triangle using the formula base * height / 2. You have base = 10 and height = 7, so area = 7 * 10 /2 = 70/2 = 35. Since you're finding the combined area of 4, you have to do 35 * 4 = 140.
Part 2: To do this, find the side length of the square. Looking at the picture, you see that all you have to do is 10 + 7 = 17 to find one side. Then, to find the area do 17 * 17 = 289.
Part 3: To find the area of the small square, all you do is area of the large square - combined area of 4 small triangles, so 289 - 140 = 149.
Part 4: a^2 = 7 * 7 = 49. Then, b^2 = 10 * 10 = 100. Adding them together, you get 100 + 49 = 149.
Part 5: Since you already have the a^2 + b^2 part, all you need to do is find what c^2 is. You can see in the picture that c^2 equals the area of the small square, which you found in part 3. c^2 = 149. Then, you have 149 and 149, which are equal so the answer is =.
the base of a rectangular prism has an area of 1 over 8 ft2 and the height of the prism is 2 over 3 ft. what is the volume of the prism?
Answer: the volume is 1/12 ft³
Step-by-step explanation:
Multiply the area of the base times the height:
1/8 × 2/3 = 2/24 or 1/12
the ft² times ft becomes ft³
So the volume is 1/12 ft³
Pensé dos números. Sumados dan 38 y restados dan 2. ¿Qué números son?
Answer:
sorry I cannot help you sir can you translate it into English
can someone explain how to solve this please my midterms tomorrow! :)
Answer:
Step-by-step explanation:
Can some one solve this
Answer:
J Monica is right
Step-by-step explanation:
Add three to both sides, divide by 4 you get x[tex]\geq[/tex]4
Answer:
J
Step-by-step explanation:
Find the length of AD if AB = 24, DE = 8, and DC = 12.
a.8
b.12
c.14
d.10
HELP PLS
Answer:
AD = 12
Step-by-step explanation:
Find the diagram attached
From the given diagram, it can be inferred that;
AB = AD+DB and AD = DB
AB = AD + AD
AB = 2AD
AD = AB/2
Given that AB = 24
AD = 24/2
AD = 12
Hence the length of AD is 12
Answer: 10
Step-by-step explanation:
I got it right after trying the answer of 12 on CAOLA
help plz
−86 + (−14) − 23 − (+22) + 16 − (−34)=
Step-by-step explanation:
the answer is -86 mark as brainliest or rate this if u found this helpful :)
Answer:
-105
Step-by-step explanation:
-86-14= -100
-100-55= -155
16+34= 50
-155+50= -105
Transform to slope-intercept form. 1+2y=6x-3
Answer: Y=3X-2
Step-by-step explanation:
First you are gonna need to combine all like factors.
1+2y=6x-3 (subtract 1 from both sides)
2y=6x-4
Then you need to get the y by itself.
2y=6x-4 (divide all terms by 2)
y=3x-2
now you are in slope intercept form (y=mx+b)
-4x < 28
does anyone know the solution and answer?
Answer:
x>−7
Explanation:
Let's solve your inequality step-by-step.
−4x<28
Step 1: Divide both sides by -4.
−4x/−4 < 28/−4
x>−7
Answer: x>−7
You park in a garage 3 floors below ground level. Then you get in the elevator and go up 12 floors. What floor do you get off the elevator?
Answer: (B) 6 floors
Step-by-step explanation: Use the equation -3 + 9 to get the amount of floors above ground level.
-3 + 9 = 6
6 floors.
If this helps may I please have a brainliest.
Answer:
you would get off at the 9th floor because in order to reach ground level again your would already go up 3 of the 12 floors. leaving 9 floors left to go up.
Step-by-step explanation:
-3+12=9
which equation has a solution x= -3
A) 2x - 7 = -1
B) 3x + 8 = 1
C) 1/2x + 8 = 10
D) 1/2(2x - 6) = -6
Answer:
D
Step-by-step explanation:
1/2 ( 2x - 6) = -6
1/2 = 0.5
0.5(2x-6) = -6
1x-3=-6
1x=-6+3
x=-3/1
x=-3
What’s the volume of this cube?
Answer:
Formula: V = a^3
a = 2in
Input: V = a^3 = 2^3 = 8
Step-by-step explanation:
Solve for x.2(-x - 4) = 4x + 16
a) 4
b) 3
c) -3
d) -4
Answer:
44
Step-by-step explanation:
Answer:
X=-4Step-by-step explanation:
First, we must solve for the parenthesis so...
-2x-8=4x+16
Then we must simplify this even more so lets add the 8 to 16
-2x=4x+24
Then we must subtract 4x from -2x
-6x=24
we must now divide 24 by -6 so we can isolate the x
x=-4
I hope this helped :)
The residents of a village want to paint a sign that shows the elevation of their village to the sea. Their altimeter shows +2,100 feet. What should their signboard read?
Answer:
Wassss uppppp
Step-by-step explanation:
i dont know
A baseball player earns $3 million in 2015. During the next 15 years, the earnings increase 4% each year.
a. Write an exponential growth model giving the earnings y (in millions of dollars) t years after 2015. Write the base of the model as a decimal.
An exponential growth model is y=
b. In which year will the player's earnings first exceed $5,000,000?
Answer:
[tex]y=3*1.04^{t}[/tex]
in 2029
Step-by-step explanation:
[tex]y=3*1.04^{t}[/tex]
[tex]when y=5\\t=\frac{ln(5/3)}{ln(1.04)} =13.02 ..[/tex]
have to round it up to 14 to exceed
3/11 as a decimal equivalent
Answer:
The decimal form for this is 0.27 (With a line on top of it.)
Step-by-step explanation:
See this image:
Daniel wants to know the volume of his cube. He notices that the cube 1/5 centimeters side lengths. What is the volume of the cube?
Answer:
1/125 cm^3
Step-by-step explanation:
Given data
Length of one side = 1/5cm
Required
The volume of the cube
We know that
V= l^3
substitute
V= (1/5)^3
V= 1/125cm^3
Hence the volume is 1/125 cm^3
4w − 18 = 18 solve for w
Answer:
hello! :) have a good day!
W = 9
help me please I need help
Answer:
D) 6 in x 4 in
Step-by-step explanation:
3" x 2" scaled up to 1:20 would be 60" x 40"
60" x 40" scaled back to 1:10 would be 6" x 4"
also the scale factor 1:20 is double the scale factor of 1:10