Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ?

f(x)= x3 - 2x2 - 3x + 6
f(x)= x3 - 2x2 + 3x + 6
f(x)= x3 + 2x2 - 3x + 6
f(x)= x3 + 2x2 - 3x - 6

Answers

Answer 1

Using the factor theorem, it is found that the polynomial is:

[tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex]

Given by the first option

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

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] using the factor theorem it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

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

In this question:

[tex]x_1 = 2[/tex][tex]x_2 = \sqrt{3}[/tex][tex]x_3 = -\sqrt{3}[/tex]By the options, leading coefficient [tex]a = 1[/tex]

Thus:

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

[tex]f(x) = (x - 2)(x^2 - 3)[/tex]

[tex]f(x) = x^3 -2x^2 - 3x + 6[/tex]

Which is the polynomial.

A similar problem is given that: https://brainly.com/question/4786502


Related Questions

15. In a class of 40 students, 15 passed in Mathematics and Science both and 20 passed in only one subject. How many students failed in both the subjects? (A) 5 (B) 25 (C) 20 (D) 45​

Answers

The answer may be A.

A bus leaves Islamabad at 11:00 am and reaches Lahore at 3:00 p.m . If the distance bwtween Islamabad to Lahore is 380km , find the speed od the bus.​

Answers

Answer:

Step-by-step explanation:

Hello!

11h-> 3h

=> 4h

380/4 =>95km/h

Mrs. hilt baked 7 dozen cookies and sold them for $4.25 per half dozen. how much money would Mrs. Hilt make if she sold all the cookies?

Answers

Answer:

59.5

Step-by-step explanation:

Half dozen = $4.25

Full Dozen = 2 X (4.25)

= 8.5

7 Dozens price = 7 X 8.5 =

= $59.5

Answered by Gauthmath

You plan to cut a board into 3 pieces to repair part of a railing. You are going to cut the two ends of the board off into two equal pieces that are 3.2 feet long, if the remaining piece needs to be 0.66 times longer than the each of the first two cuts what length board should you buy? Round to the nearest tenth.​

Answers

Answer:

11.2

Step-by-step explanation:

3.2 / 0.66 = 4.8484...

3.2 + 3.2 + 4.8484... = 11.24848...

= 11.2 (rounded)

Brainliest, please!

please help me with this trigonometric ratio/terminal arm question, giving brainliest!

Answers

Here is the first half

Find the length of the side and area ot the square whose perimeter is given below a)44cm b)80cm​

Answers

9514 1404 393

Answer:

  a) 11 cm

  b) 20 cm

Step-by-step explanation:

A square has four equal-length sides, so the perimeter is 4 times the side length. Then the side length is 1/4 of the perimeter.

  a) s = (1/4)(44 cm) = 11 cm

  b) s = (1/4)(80 cm) = 20 cm

If A is directly proportional to B and B = 5 when A = 6.
(a) Find the value of B when A=4.
(b) Find the value of A when B = 2.
(c) Sketch the graph of A against B.


Answers

Answer:

good question

but I don't know

please I am so sorry


Identify the correct statement for the given figure.

Answers

Answer:

B

Step-by-step explanation:

b/c the figure is right angle

Answer:

[tex]x = \frac{83}{7} [/tex]

Step-by-step explanation:

5x+(2x+7)=90

7x+7=90

7x=90-7

7x=83

x=83/7

x=11.857

Factor completely, show work.

x² - 49

Answers

You want to pull out the square roots of each term since they are both perfect squares.

Factor using the difference of squares formula: a2-b2=(a+b)(a-b)

This formula allows the middle term to cancel out.

=x2 - 49

=(x + 7)(x - 7)

ANSWER: (x + 7)(x - 7)

Hope this helps! :)

what's the rational approximation of 15​

Answers

Answer:

15 / 1

hope that helps uh...

toán lớp 8
giải bất phương trình: 2x + 2 > 4

Answers

Answer:

x>1

Step-by-step explanation:

Answer:

x>1

I hope it will help you

Instructions: Solve the triangle, find mA and mZC.

Answers

Step-by-step explanation:

mA=cosA=17/38

A=cos inverse of 17/38

A=63 degrees

Một lớp có 40 học sinh gồm học sinh giỏi, học sinh khá , và học sinh trung bình , số hs trung bình chiếm 1/4 cả lớp , số hs khá bằng 60% số học sinh còn lại a) tính số học sinh mỗi loại B) tổng số hs khá và giỏi chiếm bao nhiêu phần trăm trong lớp

Answers

Answer:

Đổi 60% = 3/5

a) Số học sinh trung bình là:  40 * 1/4 = 10 (hsinh)

Tổng số hsk và hsg là:  40 - 10 = 30 (hsinh)

Số học sinh khá bằng 60% số học sinh còn lại nên số hsk là:

             30 * 60% = 18 (hsinh)

Số học sinh giỏi là:  30 - 18 = 12 (hsinh)

b) Tổng số hs khá và giỏi chiếm số phần trăm trong lớp là:

             30 : 40 * 100 = 75%

surface area of cylinder

Answers

Answer:

The answer is C. [tex]256\pi[/tex] [tex]in^2[/tex].

Step-by-step explanation:

To solve for the surface area of this cylinder, start by using the cylinder surface area formula, which is [tex]SA=2\pi rh+2\pi r^{2}[/tex]. Next, plug in the information given from the problem into the formula, which will look like [tex]SA=(2)(\pi )(8in)(8in)+(2)(\pi )(8in^{2})[/tex]. Then, simplify the equation, which will look like [tex]SA=(128in)(\pi) +(128in)(\pi)[/tex]. The next step is to simplify the equation further, which will look like [tex]SA= 256\pi[/tex] [tex]in^{2}[/tex]. The final answer is [tex]256 \pi[/tex] [tex]in^2[/tex].

Can you please factor the problems below and explain/show all your steps. I will be attaching a photo with the problems as well in case they are more understandable on there. Also if you can please explain how you used the key concepts from the photo in your work if you used them.
Factor: 2a^3 + 4a^2 + 8a
Factor: 6y^4 - 294y^2
Factor: 5x^2 + 50x +125

Answers

1) The factorization is: [tex]2a(a^2 + 2a + 4)[/tex]2) The factorization is: [tex]6y^2(y - 7)(y + 7)[/tex]3) The factorization is: [tex]5(x+5)^2[/tex]

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

To factor each expression, we apply the given concepts, that is, greatest common factor, difference of squares and perfect squares.

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

Expression 1:

The expression is:

[tex]2a^3 + 4a^2 + 8a[/tex]

First, we find the gcf of the numbers 2, 4 and 8, which is 2.

Of the exponents, the gcf between 3, 2 and 1 is 1, so:

[tex]2a^3 + 4a^2 + 8a = 2a(\frac{2a^3}{2a} + \frac{4a^2}{2a} + \frac{8a}{2a}) = 2a(a^2 + 2a + 4)[/tex]

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

Expression 2:

The expression is:

[tex]6y^4 - 294y^2[/tex]

The gcf of 6 and 294 is 6.

The gcf of the exponents 2 and 4 is 4.

Thus:

[tex]6y^4 - 294y^2 = 6y^2(\frac{6y^4}{6y^2} - \frac{294y^2}{6y^2}) = 6y^2(y^2 - 49)[/tex]

Then, applying the difference of squares:

[tex]y^2 - 49 = (y - 7)(y + 7)[/tex]

Thus, the factored expression is:

[tex]6y^2(y^2 - 49) = 6y^2(y - 7)(y + 7)[/tex]

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

Expression 3:

The expression is:

[tex]5x^2 + 50x + 125[/tex]

The gcf of the coefficients, 5, 50 and 125 is 5, so:

[tex]5(\frac{5x^2}{5} + \frac{50x}{5} + \frac{125}{5}) = 5(x^2 + 10x + 25)[/tex]

Applying the perfect square, we get that:

[tex]x^2 + 10x + 25 = (x + 5)^2[/tex]

Tus, the factored expression is:

[tex]5(x^2 + 10x + 25) = 5(x+5)^2[/tex]

A similar question is given at https://brainly.com/question/11930822

pls help me ASAP !!!!!!!!!

Answers

Hopefully this help

4.
A line contains the points R (-5, -6) S (1, 5) and T (x, 10). Solve for x. Be sure to show and explain all work

Answers

Answer:

x is 3.[tex]\overline{72}[/tex]

Step-by-step explanation:

The given points on the line are;

R(-5, -6), S(1, 5) and T(x, 10)

The number of points required to find the equation of the line = 2 points

The slope, m, of the line using points R(-5, -6) and S(1, 5) is given as follows;

m = (5 - (-6))/(1 - (-5)) = 11/6

The equation of the line in slope and point form, using point S(1, 5) is therefore;

y - 5 = (11/6)·(x - 1) = 11·x/6 - 11/6

y - 5 = 11·x/6 - 11/6, given that the x-value is required, we have;

x = (y - 5 + 11/6) × 6/11 = 6·y/11 - 19/11

x = 6·y/11 - 19/11

At point T(x, 10), y = 10, therefore, we have;

x = 6×10/11 - 19/11 = 41/11 = 3.[tex]\overline{72}[/tex]

x = 3.[tex]\overline{72}[/tex].


What is the greatest common factor of 15n^5, 30n^3, and 45n^2

Answers

Answer:

15n^2 as it the highest expression that is common among these three.

The greatest common factor is 15.

i need help plsssssssss

Answers

Answer:

are you look for finaincl loan

Step-by-step explanation:

i think i got the hang of it but i still need help

pls help !​

Answers

Answer:

50

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180 degrees

since one of the angle is given as 80 the remaining is 100

The given is an isosceles triangle which means two of its side length and so its angles are equal in measure so 100/2 = 50

Answer:

4/5 t

Step-by-step explanation:

why?

80%xt by definition of p%=p/100

80/100t

80/100t reduce the fraction with 20

so the answer is;

4/5 t

Hope it helps

What are the solutions of the following system?

Answers

Answer:

(0,-5) and (-4,3) are the points to the equations.

Step-by-step explanation:

Solution:

Step 1: Make an equation for y to substitute to the first equation.

x^2+y^2=25

y=-2x-5

Step 2: Substitute the y-value to the first equation.

x^2+(-2x-5)^2=25

x^2+4x^2+20x+25=25

Our x-values would be 0, and -4.

Step 3: Solve for the y-values by substituting 0 and -4 to the equation y=-2x-5.

y=-2(0)-5=-5 and makes the ordered pair (0,-5)

y=-2(-4)-5=3 and makes the ordered pair (-4,3)

Therefore our answers would be (0,-5) and (-4,3)

Answer:

(-4;3), (0;-5)

Step-by-step explanation:

In a biconditional statement, the output is true if at least one input is true.

-true
-false

Answers

In a biconditonal statement the output is true if at least one input is true….this is false.

Which are the solutions of x2 = –13x – 4?

Answers

Answer:

The 3rd dot and 4th dot, you should select to get the correct answer.

3. Find the measure of angle A.

Answers

Answer:

20

Step-by-step explanation:

Angle Formed Outside = 1/2(difference of Intercepted Arcs)

The outside arc = 360-160 = 200

A =1/2 (200-160)

A = 1/2 (40)

A = 20

Please help me find x
Need help fast!!

Answers

Answer:

x = 100°

Step-by-step explanation:

p and q are parallel lines. Construct line 'l' parallel to p and q

a = 30°   {p// l  when parallel lines are intersected by transversal alternate interior angles are congruent}

c +110 = 180  {linear pair}

c = 180  - 110

c = 70°

b= c   {q // l  when parallel lines are intersected by transversal alternate interior angles are congruent}

b = 70°

x = a + b

x = 30° + 70°

x = 100°

A group of friends is addressing wedding invitations. Casey can address 22 envelopes in one hour, Anne can address 48 envelopes in two hours, and Paula can address 62 envelopes in three hours. About how long will it take them to address 420 envelopes?

A.
19.09 hours
B.
22.00 hours
C.
7.24 hours
D.
6.30 hours

Answers

Answer:

D

Step-by-step explanation:

Let's say that we have x amount of hours.

Casey addresses 22 envelopes per hour. Another way of writing this is that for x hours, Casey addresses 22 envelopes. Therefore, given x hours, Casey addresses 22 * x envelopes.

Anne can address 48 envelopes in 2 hours. It is important to note that this is for 2 hours. To make this per 1 hour, we can write

48 envelopes = 2 hours

divide both sides by 2

24 envelopes = 1 hour.

Therefore, given x hours, Anne addresses 24 * x envelopes.

Paula can address 62 envelopes in 3 hours, so

62 envelopes = 3 hours

divide both sides by 3

62/3 envelopes = 1 hour

Given x hours, Paula can address 62/3 * x envelopes.

Adding all of these up, given x hours, the group of friends can address

22 * x + 24 * x + 62/3 * x envelopes. Because the variables are all the same (x), we can add up the coefficients, resulting in

(22 + 24 + 62/3) * x = (46 + 62/3) * x envelopes given x hours

We want to figure out the amount of hours (x) for 420 envelopes. The total amount of envelopes is equal to (46 + 62/3) * x, so we set 420 equal to that, resulting in

(46 + 62/3) * x = 420

divide both sides by (46 + 62/3) to isolate x

420 / (46 + 62/3) = x

= 6.3 hours

find the area of circle having its radius 15cm​

Answers

Answer:

A≈706.86

Step-by-step explanation:

welcome to brainly

Answer:

Let π =22/7

area of circle = πr²

= 706.86

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

PLEASE HELP WILL MARK BRAINLIEST

Answers

Answer:

C

Step-by-step explanation:

Its the only answer where the y intercept is 16.

We know its 16 because the line crosses the y axis at 16

Consider these four statements about a line that passes through two points on a plane.
Statement A: The lines on a different plane from the points.
Stament B: The line lies in only one plane.
Statement C: The line is on the same plane as the points.
Statement D: The line passes through only one plane.


Which statement is true? ​

Answers

Answer:

4

Step-by-step explanation:

Not quite sure how to solve

Answers

Hi again! Sorry my work is messy but I hope u understand. I got 126 as my answer and 14/5 is the scale factor
Other Questions
Exploring the Electromagnetic SpectrumAssemble the electromagnetic spectrum by dragging each piece to the correct place on the wavelength scale.Visible10-210-71010-910-5Wavelength (cm)(PLEASE HELP!!) 1. Write a brief description of one of the following: (a) fishermen at work by the sea (b) a flooded street (c) a cinema lobby just after a show (d) the street where your school is situated which on(e) a quiet evening at the beach (f) the beach on Sunday (g) the view from the window of your house/flat (h) a bus-stop in town during the rush hour (i) the market near your house please mark me brainliest please(j) a harbour scene What is another name for data?A) square rootB) additionC) subtractionD) information Bugaboo Co. manufactures three types of cookies: Fluffs, Crinkles, and Snaps. The production process is relatively simple, and factory overhead costs are allocated to products using a single plantwide factory rate based on direct labor hours. Information for the month of May, Bugaboo's first month of operations, follows: Budgeted Unit Volume Direct Labor Hours per unitFluffs 80,000 boxes 0.10Crinkles 60,000 boxes 0.20Snaps 20,000 boxes 0.50Bugaboo has budgeted direct labor costs for May at $8.50 per hour. Budgeted direct materials costs for May are: Fluffs, $0.75/unit; Crinkles $0.40/unit; and Snaps $0.30/unit.Bugaboo's budgeted overhead costs for May are:Indirect Labor $280,000Utilities $65,000Supplies $45,000Depreciation $30,000Total $420,000Assume that Bugaboo sells all the boxes it produces in May. Round your answers to two decimal places, if necessary.a. Compute Bugaboo's plantwide factory overhead rate for May.$_______per direct labor hourb. Compute May's product cost for each type of cookie.Cost per box Fluffs Crinkles SnapsTotal manufacturing cost $____ $____ $ ____ write a hindi poem on independence day (self conposed)(dont copy even a line) Who painted the image above? WHAT IS the side that is against the debate topic The process of diffusion can be described as: Movement of water from the area of high concentration of solute to the area of low concentration of solute. Movement of solute from the area of low concentration of solute to the area of high concentration of solute. Movement of water from the area of low concentration of solute to the area of high concentration of solute. Movement of solute from the area of high concentration of solute to the area of low concentration of solute. Which method of farming in the South offered poor white and African American farmers the most control oftheir labor and harvest?A. plantation farmingB. sharecroppingC. share-tenancyD. tenant farming write a letter to your uncle telling him about your friend in french Find the volume of the prism. Round to the nearest tenth. Please help! Identify which of the following is not equivalent to a1/4Answers (images below)no links please! Please help me anyone what is the build in libary function to compare two strings? Which was a major effect of Pope Leo III crowning Charlemagne emperor of the Romans ? *(30 points)* One pump can fill a tank of water in 2 hours. A second tank can fill the same tank in 3 hours. If both pumps are used together, how long will it take to fill the tank? Find the Algebric Equation The sum of the product of 5 and a number, and 8 Given that S=n/2(2a+(n-1)d). If a=4,d=3 and n=20 find the value of S What number should be added to -3/2 to get -5/8 13. The word 'REC' stands for A. Resident Electoral Commissioner B. Representatives of Electoral Commission C. Regional Electoral Commissioner D. Regional Electoral Commission