Find all of the roots of the following quartic equation:
h(x)= x^4 - 2x^3 - 9x^2 + 18x

Answers

Answer 1
x4)-(2•(x3)))-32x2)+18x
STEP
2
:

Equation at the end of step
2
:

(((x4) - 2x3) - 32x2) + 18x
STEP
3
:

STEP
4
:
Pulling out like terms

4.1 Pull out like factors :

x4 - 2x3 - 9x2 + 18x =

x • (x3 - 2x2 - 9x + 18)

Checking for a perfect cube :

4.2 x3 - 2x2 - 9x + 18 is not a perfect cube

Trying to factor by pulling out :

4.3 Factoring: x3 - 2x2 - 9x + 18

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -9x + 18
Group 2: x3 - 2x2

Pull out from each group separately :

Group 1: (x - 2) • (-9)
Group 2: (x - 2) • (x2)
-------------------
Add up the two groups :
(x - 2) • (x2 - 9)
Which is the desired factorization

Trying to factor as a Difference of Squares:

4.4 Factoring: x2 - 9

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3
Check : x2 is the square of x1

Factorization is : (x + 3) • (x - 3)

Final result :
x • (x + 3) • (x - 3) • (x - 2)

Related Questions

Juliette made cookies for a bake sale and wants to package the same number of cookies together. If she makes 16 chocolate chip cookies, 32 mint cookies, and 24 gingerbread cookies, what is the most number of each type of cookie that will be in the bag?

Answers

Answer:

8 cookies

Step-by-step explanation:

We are asked in the above question to find the most number of cookies that would be in the bag.

We solve the above question using the Greatest Common Factor method

We find the factors of 16, 24, 32

The factors of 16 are: 1, 2, 4, 8, 16

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 32 are: 1, 2, 4, 8, 16, 32

Then the greatest common factor is 8.

Therefore, the most number of each type of cookie that will be in the bag is 8 cookies

Name the central angle of the given arc.

Answers

Fe hi
This is the answer

Standard
Expanded
Written
6000 + 900 + 10 + 5

Answers

Answer: This is written in Expanded form.

Step-by-step explanation: The number is 6,915, to write a number in expanded form, write it's place values by the number it's in.

Ex: Expanded form of 5,731: 5,000 + 700 + 30 + 1

whats 3472532*67 then divided by 3? Thank you! -Ibuki

Answers

Answer:

77,553,214.66666667

Step-by-step explanation:

calculater

Answer:

77553214 2/3

Step-by-step explanation:

i squeezed out the baby yet i have no idea who the father is

Math Help plz. I cant figure it out.

Answers

Answer:-1 1/3 because 5 1/3+-4 1/6 is like subtracting them as a positive and you get 1 1/6 then subtract 2 1/2 to get -1 1/3

Step-by-step explanation:

What is the value of the expression? 18 - 2 x (4 + 3)

Answers

Answer:

=−14x+18

Step-by-step explanation:

happy to help ya :)

Answer:

112

Step-by-step explanation:

so you split the question by doing 18 - 2 then do 4 + 3 then you mutiply the answer

A) describe each two-dimensional figure cross section that results from slicing each three-dimensional figure
B)describe the two dimensional figure cross section that results from slicing the cylinder number 6 with a vertical cross-section
PLEASE HELP QUICK
I WILL MARK BRAINLYIEST'

Answers

AnswerWE  NEED MORE

Step-by-step explanation:

Hans opens a circular window that is 3.5 feet across at its widest point. What is the circumference of the window to the nearest whole number? Use 3.14 for π. help pls

Answers

Answer: 11

Step-by-step explanation:

i did 3.5 x 3.14 = 10.99 and rounded to the nearest whole number, 11.

The circumference of the circular window to the nearest whole number is 11 feet.

What is a circle?

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is pir^2.

We have,

To find the circumference of the circular window, we need to use the formula:

C = πd

where C is the circumference, π is the constant pi, and d is the diameter of the circle.

Since the window is 3.5 feet across at its widest point, the diameter of the circle is also 3.5 feet.

Plugging in the value of the diameter in the formula, we get:

C = πd

C = 3.14 x 3.5

C = 10.99

Rounding the result to the nearest whole number, we get:

C ≈ 11 feet

Therefore,

The circumference of the circular window to the nearest whole number is 11 feet.

Learn more about circle here:

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y=x-2
make x the subject

Answers

Answer:

x + 2 = y

Step-by-step explanation:

y = x - 2

x = y - 2

x + 2 = y

Answer:

x=y-2

Step-by-step explanation:

x equals y -2 that is the answer to this equation

Calculate the vapor pressure (in torr) of a solution containing 0.2 moles of solute dissolved in 10 moles of water at 25°C. Vapor pressure of pure water at 25°C is 23.8 torr. Enter text here Enter 2021 Acellus Corporation. All Rights Reserved. C​

Answers

Answer:

the vapor pressure of a solution at 25°C that contains 76.6 g of glucose (180.2 g/mole) in 250.0 mL of water. The vapor pressure of pure water at 25°C

Step-by-step explanation:

your answer is:  22.9 torr at 25°C

Explanation:

When a non volatile solute is added to a pure solvent, the vapour pressure of the mixture decrease regard to the pure solvent following the equation

Where vapour pressure of the pure solvent (Water) is 23.8torr at 25°C.

Mole fraction of water is the ratio between moles of water and total moles in solution. The solution has a mole fraction of water of:

Replacing in Raoult's law:

Vapor pressure of the solution is 22.9 torr at 25°C

hope this helps!

Find the total surface area of a cylinder whose diameter is 28 cm and height is 11 cm.

Answers

59 cm yun ang sagot sa tanong mo

Answer:

2199.11 (with pi)

2198 (with 3.14)

Step-by-step explanation:

A=2πrh+2πr²

A=2π(14)(11)+2π(14)²

A=2π(154)+2π(196)

A=2(483.56)+2(615.44)

A=967.12+1230.88

What is the measure of N

Answers

Answer:

No picture sorry

Newtons are a measurement of force. By definition, 1 N is the amount of force required to accelerate an object of mass 1 kg to 1

please mark in brain list


1
5
5.0,
71
1. -0.3, 4.33, -12, 10001, -12, -2017, 4
From the given numbers, list the numbers that are
(i) positive integers, (ii) negative integers,
(iii) positive numbers, (iv) negative numbers.​

Answers

Answer:

positive number

Step-by-step explanation:

because I got it right

Can yall help its due in 30 minutes

Answers

Answer:

18%

Step-by-step explanation:

540$ is 18% of what he put towards the loan :))

I need help with this please

Answers

Answer:

Car B is going faster

Step-by-step explanation:

Car B has a higher rate.(It goes 20 more miles per hour)

Please help i will give brainly FIRST PERSON TO GET IT RIGHT EVERY TIME I POST A QUESTION YOU WILL ALWAYS GET BRAINLY

Answers

What he said


Hope this helped

The cost of hiring a surfboard involves an up-front fee plus an hourly rate. Three hours of hire costs $50 and 7 hours costs $90. Sketch a graph of costs, $C, for t hours of hire using the information given above. ​

Answers

Answer:

...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Tobey, Finn, and Mary rode their bicycles in the park.
Tobey: 432 yards
Finn: 1,300
Mary: 1/4 mile
Who rode the furthest? Explain how you know.

Answers

Answer: Mary

Step-by-step explanation:

Tobey 432 yards is 1296 foots

Mary 1/4 mile is 1320 foots

You didnt mark what kind of measurment Finn has but I assume it's foots, then Mary wins!

(Tobey 1296)

(Finn 1300)

(Mary 1320)

Answer:

Yeah it's Mary

Step-by-step explanation:

Amelia's account balance is $16. If she uses her debit card to buy a $32
shirt from the mall, what will the balance of her account be?

Answers

Answer:

-$16

Step-by-step explanation:

16-32=-16

the total surface area of this cuboid is 76cm^2 find the value of x (5cm = width, 4cm= length and x = height)

Answers

Answer:

Height x=2

Step-by-step explanation:

area of top & bottom:

(5)(4)(2)=40

area of 2 sides:

(x)(5)(2)=?

area of the other two sides:

(x)(4)(2)=?

total area=76

76=40+10x+8x

simplify:

36=18x

x=2

8.12
Given the diagram below, what is cos(45") ?
450
Triangle not drawn to scale
A. 2-3
B. 4/2
C.
D. JE

Answers

B is the correct answer

The value of  cos 45° in the given triangle is 1/√2, Option C is correct.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In the given right triangle the hypotenuse is 8√2

In the given triangle the two legs are equal.

Let x be the length of the two legs

By Pythagoras theorem, let us find the length of a leg.

x²+x²=(8√2)²

2x²=64(2)

2x²=128

Divide both sides by 2

x²=64

Take square root on both sides

x=8

Now let us find the cosine function, the ratio of adjacent side and hypotenuse

cos45 = 8/8√2

=1/√2

Hence, the value of  cos 45° in the given triangle is 1/√2, Option C is correct.

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To keep her pet groundhog Marley happy, Gwen built a rectangular pen for Marley with an area of 242 square feet. She only had 66 feet of fencing to use, and wanted the length to be twice as long as the width. What are the dimensions of the pen?

Answers

seitz seirz seitz seit

each side of a triangle is nine inches long. find the perimeter

Answers

The triangle in which the side are nine inches long has a perimeter of 27 inches.

Perimeter of a triangle

The perimeter of a triangle is the sum of the length of the whole side.

The triangle have three sides and the perimeter is the sum of the whole sides.

According to the question, the triangle has the whole sides as 9 inches.

This means the triangle is an equilateral triangle.

Therefore,

length of side = 9 inches

perimeter = 9 + 9 + 9

perimeter = 27 inches

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Felipe planted some seeds for a science project. One of his plants grew 6 2/7 inches in the first week, and then it grew 5 11/14 inches during the second week. How much did the plant grow during these two weeks? The answer should be written as a proper mixed number and should be simplified, if possible.

Answers

Answer:

The plant grew [tex]12\frac{1}{14}[/tex] inches

Step-by-step explanation:

Operations with Fractions

Felipe planted seeds for a science project. One of the plants grew 6 2/7 inches in the first week and 5 11/14 inches in the second week.

We are required to find the total growth during the two weeks. We have to find the sum of:

[tex]6\frac{2}{7}+5\frac{11}{14}[/tex]

Let's convert both fractions to improper form:

[tex]6\frac{2}{7}+5\frac{11}{14}=6+\frac{2}{7}+5+\frac{11}{14}[/tex]

Adding the integers:

[tex]6\frac{2}{7}+5\frac{11}{14}=11+\frac{2}{7}+\frac{11}{14}[/tex]

Now we find the LCM of 7 and 14 is 14, thus:

[tex]6\frac{2}{7}+5\frac{11}{14}=11+\frac{4}{14}+\frac{11}{14}[/tex]

[tex]6\frac{2}{7}+5\frac{11}{14}=11+\frac{15}{14}=11+\frac{14+1}{14}[/tex]

[tex]6\frac{2}{7}+5\frac{11}{14}=11+1+\frac{1}{14}[/tex]

[tex]6\frac{2}{7}+5\frac{11}{14}=12+\frac{1}{14}[/tex]

Rewriting as a mixed number:

The plant grew [tex]12\frac{1}{14}[/tex] inches

Janie ordered boxed lunches for a student advisory committee meeting. Each lunch costs $4. The total cost of the lunches is $47, including a $7 delivery fee. Write and solve an equation to find x, the number of boxed lunches Janie ordered.

Answers

Answer:

10 lunches

Step-by-step explanation:

$47-$7=$40

40/4=10

Hello, 928747!

So we are trying to find how many boxed lunches Janie ordered.

Each box is $4.00 and the total cost is $47.00 + delivery fee of $7.00

So to find this, we will first subtract the delivery fee because that does not count towards the lunches.

47 - 7 = 40

So the boxed lunches cost $40.00

To find how many Janie ordered, we will divide 4 by 40

40 ÷ 4 = 10

So Janie bought 10 boxed lunches.

The equation would be (47 - 7) ÷ 4

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GUYS HELP
-5 = -11 + 2m

Answers

Isolate the variable by dividing each side by factor that don’t contain the variable m=3

Mr. Smith wants to order some pizza and cheese pizza cost $11 and pepperoni pizza cost $12.50 if you bought 13 pieces total and paid $153.50 how many pepperoni pizza did he buy

Answers

Answer: Mr Smith bought 7 pepperoni pizza

Step-by-step explanation:

Step 1

cost of cheese pizza  =$11

pepperoni pizza cost =$12.50

let number cheese pizza be represented as c

and number of pepperoni pizza be represented as p

such that the total number of pizza  bought which equals 13 can be represented as

c+ p= 13

and total cost of both pizza  can be expressed as

11c+ 12.50p =153.50

Step 2 Solving

 c+ p= 13

11c+ 12.50p =153.50

By elimination method, Multiply equation 1 by 11 and subtract the new equation from equation 2

11c+ 12.50p =153.50

11c+ 11p=143.

1.5p =10.5

p= 10.5/ 1.5 =7

c+ p= 13

c= 13-p =13-7=6

Therefore Mr Smith bought 6 cheese pizza and 7 pepperoni pizza

Write the ratio of 24 cats to 16 dogs in simplest form in 3 ways explain or show your work

Answers

Answer:

3:2

3 to 2

3/2

Step-by-step explanation:

24/16 reduces to 3/2.

Answer:

3/2  5/3 12/8

Step-by-step explanation:

20 points . I need help with this.

Answers

Answer:

1) 117

2) 51

3) congruent

4) to each other

Step-by-step explanation:

What is the product of 14.5 and 20.2?

Answers

Answer:

292.9

Step-by-step explanation:

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