Mathematics High School

Factor the polynomial expression 3x2+2.
A. (3‾√x+2‾√i)(3‾√x−2‾√i)
B. (3‾√x+i)(3‾√x−i)
C. (3‾√x+2‾√)(3‾√x−2‾√)
D. (3x+2‾√i)(3x−2‾√i)

Answers

Answer 1

Using the Factor Theorem, the expression 3x² + 2 is factored as follows:

[tex]3x^2 + 2 = (\sqrt{3}x + i\sqrt{2})((\sqrt{3}x - i\sqrt{2}))[/tex]

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this problem, the expression is:

3x² + 2.

The roots are found as follows:

[tex]3x^2 + 2 = 0[/tex]

[tex]x^2 = -\frac{2}{3}[/tex]

[tex]x = \pm \sqrt{-\frac{2}{3}}[/tex]

[tex]x_1 = -i\sqrt{\frac{2}{3}}[/tex]

[tex]x_2 = i\sqrt{\frac{2}{3}}[/tex]

Hence the factored expression is:

[tex]3x^2 + 2 = \left(x + i\sqrt{\frac{2}{3}}\right)(x - 1\sqrt{\frac{2}{3}}\right) = (\sqrt{3}x + i\sqrt{2})((\sqrt{3}x - i\sqrt{2}))[/tex]

More can be learned about the Factor Theorem at https://brainly.com/question/24380382

#SPJ1

Related Questions

what is m3 + 9n when m = 4 and n = 5

Answers

I believe the answer is 57
I believe the answer is 57.

8(333.1)I need help please

Answers

Answer:

2664.8

Step-by-step explanation:

simplify the expression -8x + 27/9

Answers

Answer:

-8/9x + 3

Step-by-step explanation:

(-8x + 27)/9

divide 9 on both side

-8/9x + 3

Is the relation below a function?
-3
-1
-1
3
у
0
1
2
3

Answers

Answer:

I believe it would be "y"

Step-by-step explanation:

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Answer:

I would say no!

Step-by-step explanation:

cause we cannot determine the rule of mapping so y is no an image of x

need help quick!!!!!

Answers

Answer:

x = y = 6

Step-by-step explanation:

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you.

heyyy! i haven't posted a question in a long time lolz. anyways, i really needed help with this!! if you can answer my question i'll give brainliest, thank you

Answers

2 ones and 8 hundredths

00.00
the first zero is tens, ones, and after the decimal, to the right is the tenths, hundredths and so on

pls help quick the blue lines at the bottom are the answer choices​

Answers

the answer is the third option

A store sells three different packs of the same yogurt. Which pack is the best buy? A) 8 containers for $4.04 B) 6 containers for $3.46 c) 4 containers for $2.84

Answers

Answer: C) 4 containers for $2.84

Step-by-step explanation:

8/4.04=1.98

6/3.46=1.73

4/2.84=1.41: best value

A, I think because if you divide the price by the amount you can see that a is the cheapest since it’s 50 cents per container

Students from Williams Middle School are also recycling aluminum cans. The data for the numbers of cans brought in each school day for a month were divided by quartiles and summarized in the box plot. Use the drop-down menus to choose the median, interquartile range, and range.

A box plot. The number line goes from 8 to 30. The whiskers range from 10 to 28, and the box ranges from 16 to 20. A line divides the box at 18.

Median:
Interquartile range:
Range:

Answers

Answer:

Median is: 18

Interquartile range: 4

Range: 18

Step-by-step explanation:

hope this helps!

What is Cos^-1( -sq2/2)? Pleaseee help ASAPOL

Answers

Answer:

s cos^(-1)(-(q^2 s)/2) + sqrt(4 - q^4 s^2)/q^2 + constant

Step-by-step explanation:

Take the integral:

integral cos^(-1)(-(q^2 s)/2) ds

For the integrand cos^(-1)(-(q^2 s)/2), substitute u = -(q^2 s)/2 and du = -q^2/2 ds:

= -2/q^2 integral cos^(-1)(u) du

For the integrand cos^(-1)(u), integrate by parts, integral f dg = f g - integral g df, where  

f = cos^(-1)(u), dg = du, df = -1/sqrt(1 - u^2) du, g = u:

= -(2 u cos^(-1)(u))/q^2 + 2/q^2 integral-u/sqrt(1 - u^2) du

Factor out constants:

= -(2 u cos^(-1)(u))/q^2 - 2/q^2 integral u/sqrt(1 - u^2) du

For the integrand u/sqrt(1 - u^2), substitute p = 1 - u^2 and dp = -2 u du:

= -(2 u cos^(-1)(u))/q^2 + 1/q^2 integral1/sqrt(p) dp

The integral of 1/sqrt(p) is 2 sqrt(p):

= (2 sqrt(p))/q^2 - (2 u cos^(-1)(u))/q^2 + constant

Substitute back for p = 1 - u^2:

= (2 sqrt(1 - u^2))/q^2 - (2 u cos^(-1)(u))/q^2 + constant

Substitute back for u = -(q^2 s)/2:

Answer: = s cos^(-1)(-(q^2 s)/2) + sqrt(4 - q^4 s^2)/q^2 + constant

Sally has 30 feet of ribbon. She cuts strips each of length 2 2/5 feet from the ribbon. Sally says I can cut 13 of these strips from this ribbon.

Answers

Answer: See explanation

Step-by-step explanation:

For us to know the number of strips that Sally can cut from the ribbon, we have to divide 30 feet by 2 2/5 feet. This will be:

= 30 ÷ 2 2/5

= 30 ÷ 12/5

= 30 × 5/12

= 25/2

= 12 1/2 strips

Therefore, the maximum number of strips that Sally can cut is 12 and not 13.

How many terms are in the expression?
12a-2c+6​

Answers

Answer:

3

Step-by-step explanation:

bc you can trust me

qual das inequações seguintes e equivalente à inequação -2x <4?
a) x<-2
b) x>-2
c) x<2
d) x>2​

Answers

Answer:

I dont get your question

9a + 12b + 2a
Help please !

Answers

Answer:

11a+12b

Step-by-step explanation:

9a+12b+2a=11a+12b

What is 2/3 divided by 6/12? REDUCE ANSWER TO SIMPLEST FORM. please help mark you brainiest!!!

Answers

Answer:

4/3 or 1.34

Step-by-step explanation:

2/3 ÷ 6/12

= 2/3 × 12/6

= 4/3 or 1.34

Construct a tangent to circle O at P.


​

Answers

Answer:

its called perimeter when it is near to dot its called cruve

estimate the difference
7 3/4 subtracted by 2 2/5
show your work

Answers

7 3/4 - 2 2/5
(7-2)+(3/4-2/5)
5+7/20

5 and 7/20 or 5.35

Answer:

5 7/20

Step-by-step explanation:

basically, you are going to want to turn these into improper fractions

7 3/4 = 28/4 + 3/4

        = 31/4  (no further simplification)

2 2/5 = 10/5 + 2/5

         = 12/5

now get common denominator to subtract

31/4 - 12/5

155/20 - 48/20 = 107/20

if you want this back into mixed fraction then convert

107/20 = 5 7/20

Classifying polynomial expression.

Answers

The answer are on paper.

Find y when x = 2

y = 30 - 2x​

Answers

y = 30 - 2(2)
y= 30 - 4
y = 26

9.
The equation a = 640s gives the relationship between s square miles and a acres. Pam owns 7.5 square miles of farmland. How many acres does she own?


4,800 acres

11.72 acres

1.17 acres

480 acres

Answers

[tex]a = 640s[/tex]

[tex]a = 640(7.5)[/tex]

[tex]a = 4800 \: [/tex]

She owns 4800 acres.

Answer:

4,800 acres

Step-by-step explanation:

A map has a scale factor of 0.25 inch : 50 miles. On the map, the distance of a river is 2.5 inches. What is the actual distance of the river?

Answers

Answer:

105 Miles po Sana makatutulong

i need help. what do i do and how do I solve this?

Answers


x = -11.6

-(-11.6) + 1.2 = 12.8

Isolate the variable by dividing each side by factors that don’t contain the variable.
Answer:
X= -11.6

Step-by-step explanation:

Step 1 - Subtract 1.2 from both sides.
-x + 1.2 - 1.2 = 12.8- 1.2
-x = 11.6

Step 2: Divide both sides by -1.
-x 11.6
__ __
-1 -1


If u don’t understand try searching up (solving variables on both sides calculator) It gives steps : )

Jaime had $37 in his bank account on Sunday. The table shows his account activity for the next four days. What was the balance in Jaime's account after his deposit on Thursday?

Answers

Answer:C

Step-by-step explanation:

37 +17.42-12.60-9.62+62.29 = 94.49

37+17.42-12.60-9.62+62.29=94.49
C) 94.49
Jamie broke:((

80 - [50 - {20 ÷ 2 – (16 - 2÷ 2) ÷ 3}]

Answers

80 - [50 - {20/2 - (16 - 2/2) ÷ 3}]

80 - [50 - {20/2 - (15) ÷ 3}]

80 - [50 - {10 - 5}]

80 - [50 - {5}]

80 - [45]

35

Answer:35

Step-by-step explanation:

80-[50-(10-5)

80-(50-5)

80-45=35

Find f(x) and g(x) so that the function can be described as y = f(g(x)).

y = Four divided by x squared. + 9
a) f(x) = x + 9, g(x) = Four divided by x squared.
b)f(x) = x, g(x) = Four divided by x. + 9
c)f(x) = One divided by x., g(x) = Four divided by x. + 9
d)f(x) = Four divided by x squared., g(x) = 9

Answers

the answer is Y/g

y=fgx

y/g=fx,which mines f(x)=y/g

Please hurry
Select all the points that are on the graph of the line
3x + 5y = 20 ?

Answers

Answer:

x=5

y=1

Step-by-step explanation:

3*5=15

5*1=5

15+5=20

A nurse wants to simulate the number of male and female births at the hospital where she
works using a random digit table.
Which of the following best simulates this situation?

Answers

Answer:

Let the digits 0,1,2,3 and 4 represent the birth of a boy, and let digits 5,6,7,8, and 9 represent the birth of a girl. Use a table of random digits. Choose the first 10 digits in the table and record the number of boy and girl births. Continue to choose batches of 10 digits for a total of 100 times, recording the number of boy and girl births. (possibly B)

2/3 divided by 5 (i just need to check)

Answers

Answer:

its 0.13

Step-by-step explanation: plz mark brainliest

Answer:

0.1333333

Step-by-step explanation:

16 is the geometric mean of 8 and what other number n

Answers

9514 1404 393

Answer:

  32

Step-by-step explanation:

The geometric mean relation says ...

  16 = √(8n)

  256 = 8n . . . . . square both sides

  32 = n . . . . . . . . divide by 8

The other number n is 32.

PLEASE HELP!!
Cody bought two pairs of gloves and four hats for $43. Tori bought two pairs of gloves and two hats for $30. What are the prices for the gloves and hats? Write a system of equations!

Answers

Answer:

2g + 4h = 43

2g + 2h = 30

Step-by-step explanation:

Answer:

pairs of gloves = x

hats = y

2x + 4y = 43

2x + 2y = 30

hats = $6.50

gloves = $8.50

Step-by-step explanation:

use the elimination method to solve this system.

subtract the first equation by the second.

2x + 4y = 43

- 2x + 2y = 30

--------------------

         2y = 13

y = 6.5

plug in the y value to find x

2x + 4 (6.5) = 43

2x + 26 = 43

2x = 17

x = 8.5

Other Questions
which type of microorganism feeds primarily on organic detritus from dead organisms? question 5 fit a k-nn using the training dataset. select k as 5. test the model using the test dataset report model accuracy plot roc curveIn [1] : # your code to train a 5-nn model goes in here# your code to make predictions using the test set goes in here# your code to compute accuracy rate goes in here# your code to plot a roc curve goes in here at level two, you have ________ driving privileges because of your driving experience. In each blank next to the following terms, place the identifying letter of its best description. 1. _____ Cost center 2. _____ Investment center 3. _____ Departmental accounting system 4. _____ Operating department 5. _____ Profit center 6. _____ Responsibility accounting system 7. _____ Service department A. Incurs costs without directly yielding revenues. B. Provides information used to evaluate the performance of a department. C. Holds manager responsible for revenues, costs, and investments. D. Engages directly in manufacturing or in making sales directly to customers. E. Does not directly manufacture products but contributes to profitability of the entire company. F. Incurs costs and also generates revenues. G. Provides information used to evaluate the performance of a department manager. A soap film (n = 1.33) is 766 nm thick. White light strikes it with normal incidence. What visible wavelengths will be constructively reflected if the film is surrounded by air on both sides? The nurse reviews the treatments for lower extremity peripheral artery disease (PAD). Which therapy involves percutaneous transluminal angioplasty (PTA) and cold therapy? Express 4-3 as a power with base 2 You are provided with the task to predict your dream companys quarterly revenue for the next two years. Use the quarterly data provided in Excel in Question 5.a. In Excel, make sure you show your calculation steps clearly. In Word, explain your steps verbally.b. In Word, write resulting regression model.c. Write your quarterly predictions for the next two years. When Daisy asks if the people of their hometown miss her, Nick says, "The whole town 1 pointis desolate. All the cars have the left rear wheel painted black as a mourning wreath, andthere's a persistent wail all night along the north shore." What literary device is beingshown in this exchange?O MetaphorO PersonificationO AmbiguityO Hyperbole A U. S. Electronics firm is considering moving its production abroad. Its production function isq= L^0. 8K^0. 2 (based on Hsieh, 1995), so its MPL= 0. 8^0. 2/ L^0. 2 and its MPK=0. 2L^0. 8/ K^0. 8. In the United States, w= 8$ and r=2. In Mexico, the wage is 20% lower than in the United States but the firm faces the same cost of capital: w*= $6. 40 and r*=2. What are L and K and what is the cost of producing q=100 units in both countries? In the U. S. , L isnothing:_______ equating 7x g'(y) with fy(x, y) = 7x 12y 8 tells us that g'(y) = 12y 8, and, therefore g(y) =____________ k. Integrated Potato Chips paid a $1.50 per share dividend yesterday. You expect the dividend to grow steadily at a rate of 6.50% per year forever. a. What is the expected dividend in each of the next 3 years? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected Dividend Year 1 Year 2 Year 3 b. If the discount rate for the stock is 7.00%, at what price will the stock sell? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Current price c. What is the expected stock price 3 years from now? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Future price d. If you buy the stock and plan to hold it for 3 years, what payments will you receive? What is the present value of those payments? (Leave no cells blank - be certain to enter "O" wherever required. Do not round intermediate calculations. Round your answers to 2 decimal places.) Year 2 Year 1 $ Year 3 $ DIV Selling price TI IN Total cash flow PV of cash flow sum of the PV's $ George is a salesman who drives a lot for his job. He bought his new Toyota Prius because i gets 51 MPG is an example of for both arches, the interproximal heights of contour/crests of convexities follow this pattern. group of answer choices a. for incisors, heights of contour are in the middle third. b. for molars, heights of contour are in the occlusal third. c. the mesial height of contours are less incisal/occlusal than the distal height of contours. d. the mesial height of contours are more incisal/occlusal than the distal height of contours. In a class of 25, 15 have cat , 16 have dog and 3 have neither. Find the probability that a student chosen at random has a cat and a dog. (working out too please/solution) 1. consider the following reaction, which is thought to occur in a single step. oh ch3br ch3oh br what is the rate law? Prepare accounting equation:a. Started business with Cash Rs. 250,000.b. Purchased goods amounting to Rs. 45,000 on credit from Harish .c. Goods costing to Rs.80,000 was sold for Rs.1,25,000 on credit.d. Salaries outstanding Rs. 5000e. Rent paid Rs. 50,000f. Withdrawn by owner for personal use Rs.25,000.assets = liabilities + capital In an individual with lactate dehydrogenase deficiency, would this [NAD+]/[NADH]ratio be sufficient to lead to a significant, lasting effect on glycolytic flux? Choose one: O A. No. As long as the individual was not attempting high-intensity anaerobic exercise, the mitochondrial shuttle system would quickly restore the steady-state ratio of [NAD+]/[NADH] with minimal effects on glycolytic flux. O B. Yes. NAD+ is required for the glyceraldehyde-3-phosphate dehydrogenase reaction, which is already unfavorable under standard conditions. Further reducing the concentration of NAD+ would make this reaction even more unfavorable under cellular conditions, and this reaction would therefore not be able to proceed in the forward direction. Glycolytic flux would be significantly affected as a result. C. No. The [NAD+]/[NADH] ratio has very little effect on glycolytic flux. The lactate dehydrogenase reaction is more important for preventing the buildup of pyruvate under anaerobic conditions, which can lead to inhibition of the pyruvate kinase reaction. As long as the mitochondrial oxidation reactions are able to reduce the concentration of pyruvate, the NADH concentration is not very important. O D. Yes. Glycolytic flux is very sensitive to the [NAD+]/[NADH] ratio, and any movement away from the steady- state value would cause a significant disruption to glycolytic flux. suppose r and s are relations on {a, b, c, d}, where r = {(a, b), (a, d), (b, c), (c, c), (d, a)} and s = {(a, c), (b, d), (d, a)} find the composition of relations for r s a(n) is created by an organization to accomplish a relatively narrow range of purposes within a stated or implied time horizon.