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

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Related Questions

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.

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

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.

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:

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

8(333.1)I need help please

Answers

Answer:

2664.8

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

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!

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.

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)

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

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

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

9a + 12b + 2a
Help please !

Answers

Answer:

11a+12b

Step-by-step explanation:

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

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

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

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

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

Answers

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

Find y when x = 2

y = 30 - 2x​

Answers

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

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 : )

Construct a tangent to circle O at P.


​

Answers

Answer:

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

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

Classifying polynomial expression.

Answers

The answer are on paper.

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:((

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

Answers

the answer is the third option

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

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

Answers

Answer:

3

Step-by-step explanation:

bc you can trust me

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:

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
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