Factor each completely.one zero has been given

f(x)=x^3-4x+16;-2

F(x) = X^4+ 2x^-13x^2 -10x + 40;2

F(x)=x^3-3x^2-13x+15;-3

F(x)=x^4-8x^3+19x^2-12x;3




Answers

Answer 1

The polynomials in factored form are listed below:

f(x) = (x - 3.043) · (x - 1.521 - i 1.716) · (x - 1.521 + i 1.716) f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)f(x) = (x + 3) · (x - 5) · (x - 1)f(x) = (x - 4) · (x - 3) · (x - 1) · xHow to factor polynomials

In this question we must factor polynomials as there are both numerical and analytical methods. Mathematically speaking, factoring polynomials is represented by the following formula:

[tex]\sum^{n}_{i = 0} \,c_{i}\cdot x^{i} = \prod^{n}_{i=1}(x-r_{i})[/tex], [tex]\forall\,x, r_{i}\in \mathbb{C}[/tex]   (1)

Where:

[tex]c_{i}[/tex] - [tex]i[/tex]-th Coefficient[tex]r_{i}[/tex] - [tex]i[/tex]-th Root

Regarding fourth order polynomials we can solve them by Ferrari's method and third order polynomials by Descartes' method. Then, the solutions of each polynomials are given below:

Polynomial 1 ([tex]f(x) = x^{3}-4\cdot x +16[/tex])

f(x) = (x - 4) · (x - 3) · (x - 1) · x

Polynomial 2 ([tex]f(x) = x^{4}+2\cdot x^{3}-13\cdot x^{2}-10\cdot x + 40[/tex])

f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)

Polynomial 3 ([tex]f(x) = x^{3}-3\cdot x^{2}-13\cdot x +15[/tex])

f(x) = (x + 3) · (x - 5) · (x - 1)

Polynomial 4 ([tex]f(x) = x^{4}-8\cdot x^{3}+19\cdot x^{2}-12\cdot x[/tex])

f(x) = (x - 4) · (x - 3) · (x - 1) · x

To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/17822016


Related Questions

Urgent need please hurry

Answers

52 because because the triangle is 80 degrees

simplify 5/9x4 3/5x6 3/11x6/10 and 3 4/5x7 1/2

Answers

Answer:

529/55 and 57/2

Step-by-step explanation:

Select the correct answer.
Function m is the result of a transformation on the parent tangent function.

Answers

Answer:

C

Step-by-step explanation:

General equation of a tangent function is: y=atanb(theta-c)+d

Based on the graph, it moved pi/2 to the right.

So, the answer is C.

The result of a transformation on the parent tangent function is g(x) = tan( x - (π / 3 ). The correct option is C.

What is a parent function?

A parent function in mathematics is the simplest function in a family of functions that keeps the definition of the entire family.

The general equation of a tangent function is represented as below:-

y=atanb(Ф-c)+d

Based on the graph, it moved π/2 to the right. Therefore, the result of a transformation on the parent tangent function is g(x) = tan( x - (π / 3 ). The correct option is C.

To know more about parent function follow

https://brainly.com/question/27784114

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Help help help ASAP help

Answers

Answer:

(8, -2)

Step-by-step explanation:

While reflection over x-axis, the x-coordinate remains the same  and the y-coordinate changes to it's opposite.

So,

Rx-axis =>  = (8, -2)

Consider the rectangle with width 4 ft and length 18 ft, write a ratio of the length to the width.

Answers

Answer: 18:4

Step-by-step explanation:

Ez

Answer:

9 : 2

Step-by-step explanation:

length : Width = 18 : 4

                       [tex]\sf = \dfrac{18 \ \div \ 2}{4 \ \div \ 2}\\\\=\dfrac{9}{2}[/tex]

                       = 9 : 2

Which of the following expressions does NOT represent
91 +91 + 91?
O 91(3)
O 91.3
O (91)(3)
0913

Answers

Answer:

91.3 and 0913

Step-by-step explanation:

91 + 91 + 91 is an expression that can be simplified into a multiplication problem, because there is a number being added by itself a certain amount of times. So we have to look for a multiplication problems within our answers.

Leading us up to 91(3) and (91)(3), these are both examples of multiplcation.

91.3 would happen if you were adding .3 to 91

And 0913 would happen if you added 91 and 822

The circumference of a circle is 62.8 centimeters. What is the circle's radius?
C=62.8 cm
Use 3.14 for ​.
centimeters

Answers

Hello!

To solve this exercise, we must use the formula below:

[tex]\mathrm{C=2\cdot\pi\cdot r}[/tex]

C = 62.8cmπ = 3.14r = ?

Knowing these values, let's replace them in the formula to obtain r:

[tex]\mathrm{62.8=2\cdot\ 3.14\cdot r}\\\mathrm{62.8=6.28r}\\\mathrm{6.28r=62.8}\\\\\mathrm{r=\dfrac{62.8}{6.28}}\\\\\boxed{\mathrm{r=10}}[/tex]

So, the radius of this circle is 10cm.

Hope this helps!

8. Which statement about quadrilateral is true? A All rectangles are always squares B. All trapezoids are always rhombuses C. All rectangles are always rhombuses. D. All rectangles are always parallelogram​

Answers

Answer:

I think it's D. All rectangles are always parallelogram

Step-by-step explanation:

Please mark me brainliest if correct

According to the labor statistics document, which educational level has the highest median
income?

Answers

The doctoral degree educational level has the highest median income

What are educational level?

Education level refers to the years of formal instruction received and successfully completed.

From research in 2017 for those with the highest levels of educational level (doctoral and professional degrees) income is more than triple those with the lowest level (high school diploma)

Find out more on educational level at: https://brainly.com/question/2987151

Answer: Bachelor's Degree, and Male

Step-by-step explanation:

Z
77°
P
W
X
What is the measure of arc XWZ?
OA
257°
O B. 1039
O C. 206°
O D. 1543

Answers

The answer is B.103 degrees

7*8/10 product lies between what numbers

Answers

Answer:

5 and 6.

Step-by-step explanation:

7*8 is 56. 56 divided by 10 is 5 6/10

Abdul is working on a project and has cut a number of wooden blocks of equal size that are represented by this right rectangular prism. He now needs to cover the wooden blocks on all sides with a green fabric.

How much fabric does Abdul need in order to cover 8 of these blocks?

Answers

Step-by-step explanation:

4cm×2cm×1/2=4cm³

4cm³×8=32cm³

I think the answer is 176

Step-by-step explanation:

please tell me if I'm wrong

Winston-Salem is halfway between Boone and Raleigh. Burlington is halfway between Winston- Salem and Raleigh. If Boone is located at the coordinates (-1,3) and Raleigh is at (-5, 9), what are the coordinates of Burlington?

Answers

Answer:

The answer is (-4, 15/2)

Step-by-step explanation:

Let the Boone be x, Winston-Salem be y, Raleigh be z and Burlington be m.

We are given that Winston-Salem is halfway between Boone and Raleigh. Burlington is halfway between Winston- Salem and Raleigh.

If Boone is located at the coordinates (-1,3) and Raleigh is at (-5, 9).

We will use Midpoint Formula

[tex]( \frac{x _{1} + x _{2}}{2} , \frac{y _{1} + y _{2}}{2} ) \\ [/tex]

Where,

x₁ = (-1) and x₂ = (-5)

y₁ = 3 and y₂ = 9

Now, We will find Co-ordinates of y i.e., Winston-Salem.

So,

[tex] ( \frac{( - 1) + ( - 5)}{2} , \frac{3 + 9}{2} ) \\ [/tex]

[tex]( \frac{( - 1 - 5)}{2} , \frac{12}{2} ) \\ [/tex]

[tex]( \frac{ - 6}{2} , \frac{12}{2} ) \\ [/tex]

[tex]( - 3,6)[/tex]

Here, The coordinates of y i.e., Winston-Salem is (-3, 6).

Now, We will find Co-ordinates of m i.e., Burlington.

So,

Again, Using of Midpoint Formula;

Where,

x₁ = (-3) and x₂ = (-5)

y₁ = 6 and y₂ = 9

So,

[tex]( \frac{( - 3) + ( - 5)}{2} , \frac{6 + 9}{2} ) \\ [/tex]

[tex]( \frac{( - 3 - 5)}{2} , \frac{15}{2} ) \\ [/tex]

[tex]( \frac{( -8)}{2} , \frac{15}{2} ) \\ [/tex]

[tex]( - 4 , \frac{15}{2} ) \\ [/tex]

Thus, The coordinates of Burlington is (-4, 15/2).

5th root of 0.06
please I need fast only answer ​

Answers

Answer: 0.56967905

Steps:
Raise 0.06 to the power of 1/5

0.56967905

The area of a rectangular wall of a barn is 160 square feet. Its length is 12 feet longer than the width. Find the length and width of the wall of the barn.

Answers

Answer:

Length: 20 feet
Width: 8 feet

Step-by-step explanation:

20 is 12 feet longer than 8

20 x 8 = 160

Each of 7 students reported the number of movies they saw in the past year. This is what they reported.
13, 8, 6, 6, 18, 11, 4
Find the median and mean number of movies that the students saw.
If necessary, round your answers to the nearest tenth.
(a) Median:

(b) Mean:

Answers

Answer:

A is 6

B is 9.4

Step-by-step explanation:

First you put the numbers in order. then you take the middle number of the data set. This is how you find the median. For the mean you add all of the number in the data set then divide by how many numbers are there

hellllp meeeee need help, 100 points

Answers

Answer:

Step-by-step explanation:

View the attached graph for what your image should look like.

I hope this helps or gives you a picture of what it should look like, because it's quite a long process.

Hope this helps!

Choose the number (X) that should come next in this series (1 4 9 16 X).

20
23
25
27

Answers

Answer:

25

Step-by-step explanation:

[tex]1^2=1\\\\2^2=4\\\\3^2 = 9\\\\4^2=16\\\\\text{So the next number should be}~ 5^2=25[/tex]

A group of people are fundraising, and each person raises a certain amount of money for every mile they walk. Each person's fundraising is represented below using d for the dollars that person raises and w for the miles that person walks. Select all the representations that can be described by the equation d = 2w.

Answers

Answer:

B, C, E

Step-by-step explanation:

According to coordinates on the graphs and numbers in the tables we have the following relationship:

A) d = 1/2wB) d = 2wC) d = 2wD) d is not proportional with w since 12/6  ≠ 18/10  ≠ 20/12E) d = 2w

As we see B, C and E have same relationship, matching the target.

Step-by-step explanation:

hope it's help you this answer

can someone help me with this I already answered half of all of them but I need to make sure It's right?

Answers

Answer:

C. 56.42

Step-by-step explanation:

56 is a whole number and .42 is 42 hundredths

trigonometric equations

2sin(theta) + 3 = 4

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \:2 \sin(x) + 3 = 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:2 \sin(x) = 4 - 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:2 \sin(x) = 1[/tex]

[tex]\qquad \sf  \dashrightarrow \:\sin(x) = \frac{1}{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 30 \degree \: \: or \: \: \frac{\pi}{6} \: rad[/tex]

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Find the measures of the interior angles?

Answers

Answer:

well it's says for a its 35° and B is 100° to find x it would be 180-(35+110)=x

Step-by-step explanation:

180-(35+110)=180-145=35. so x=35°

what is equivalent to 2
x
2

7
x

3
=
0

Answers

Answer:

I'm confused with this, I dont understand what you are asking.

Step-by-step explanation:

2 is equivalent with a lot of things,

1+1

3-1

92-90

7×7-47

4÷2

the list goes on...

In the past year, Jose watched 32 movies that he thought were very good. He watched 80 movies over the whole year. Of the movies he watched, what percentage did he rate as very good?

Answers

Answer:

40%

Step-by-step explanation:

Givens and Formula

% Good = (number good / total number) * 100

% Good = ?

Number Good = 32

Total Number = 80

Solution

% Good = (32 / 80) * 100

% Good = 2/5 * 100

% Good = 40%

Under a dilation, the point (2, 6) is moved to (6, 18).
What is the scale factor of the dilation?
Enter your answer in the box.

Answer quick please !!!

Answers

Answer:

3

Step-by-step explanation:

Answer: The correct answer is 3

Step-by-step explanation:

:) it should be correct have a good day!

Find the center and the radius of the circle.
(x-4)^2 + (y + 3)^2 = 74

Answers

Answer:

radius = [tex] \sqrt{74} [/tex]center = [tex](4,-3)[/tex]

Step-by-step explanation:

We would like to calculate the centre and the radius of the circle . The given equation is ,

[tex]\longrightarrow (x - 4)^2+(y+3)^2=74 [/tex]

As we know that the Standard equation of circle is given by ,

[tex]\longrightarrow (x - h)^2+(y-k)^2=r^2[/tex]

where ,

[tex](x,y)[/tex] is a point on circle .[tex](h,k)[/tex] is the centre of circle .[tex]r[/tex] is the radius of the circle .

We can rewrite the equation as ,

[tex]\longrightarrow (x-4)^2+\{ y -(-3)\}^2=(\sqrt{74})^2\\ [/tex]

Now on comparing to the standard form , we have ;

radius = [tex]r[/tex] = [tex]\sqrt{74}[/tex]center = [tex](h,k)[/tex] =[tex](4,-3)[/tex]

Graph :-

[tex] \setlength{\unitlength}{7mm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\circle*{0.2}}\put(0.2, - .1){(4,-3)}\put(-1.2,0){\vector(0,1){5}}\put(-1.2,0){\vector(0, - 1){5}}\put(-1,0.7){\vector(1,0){5}}\put(-1,0.7){\vector( - 1,0){5}}\put(0,0){\line(-1,0){2.3}}\put( - 1.2,-0.7){$\sf \sqrt{74}$}\put(2,6){$\boxed{\sf \textcopyright \: RISH4BH }$}\end{picture} [/tex]

And we are done !

We are given the equation of circle (x - 4)² + (y + 3)² = 74 , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;

So, consider the equation of circle ;

[tex]{:\implies \quad \sf (x-4)^{2}+(y+3)^{2}=74}[/tex]

Can be further written as ;

[tex]{:\implies \quad \sf (x-4)^{2}+\{y-(-3)\}^{2}=({\sqrt{74}})^{2}}[/tex]

On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows

Centre = (4, -3)Radius = √74 units

i am confused please help

Answers

Answer:

volume = lenght x width x height

v= 12x20x14

v=3,360 in³

A triangle has side lengths of 18 in., 22 in., and 29 in. Is the triangle acute, obtuse, or right?

Acute
Obtuse
Right
None of the above

Answers

Answer:  Obtuse

========================================================

Explanation:

We have a triangle with these side lengths

a = 18b = 22c = 29

Computing a^2+b^2 gets us

a^2+b^2 = 18^2+22^2 = 808

Compare this to c^2

c^2 = 29^2 = 841

Because 808 < 841, this means a^2+b^2 < c^2

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

We have three cases:

If a^2+b^2 > c^2, then the triangle is acuteIf a^2+b^2 = c^2, then we have a right triangleIf a^2+b^2 < c^2, then the triangle is obtuse

For more information, check out the converse of the Pythagorean Theorem.

Simplify sin^2x+sin^2x+tan^2x

Answers

Answer:

Step-by-step explanation:

Need help with math probelm if do 5 stars and brainly points

Answers

Step-by-step explanation:

let's first convert feet to inches

4 ft = 48 inches ( width )

6.5 ft = 78 inches ( length )

12.5 ft = 150 inches ( height )

each cube is 1/4 x 1/4 x 1/4

x-axis ( length )

78 ÷ 1/4 = 78 x 4 = 312 cubes

y-axis ( width )

48 x 4 = 192 cubes

z-axis ( height )

150 x 4 = 600 cubes

the total number of cubes fit in the closet is :

312 x 192 x 600 = 35,942,400 cubes

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