Factor the polynomial F(x) =x^3-x^2-4x+4 completely.

Part 1: Find and list all the possible roots of F(x).

Part 2: Use the remainder Theorem to determine which of the roots from Part I are roots of F(x).

Part 3:Factor the polynomial F(x)=x^3-x^2-4x+4 completely show your work.

Part 4:check your answer from Part 3 by multiplying the factors. Show your work

Answers

Answer 1

Answer:

Step-by-step explanation:

PART 1:

Possible roots by noticing the coefficient of first term:

x = 1, -1

PART 2:

1 | 1  -1  -4   4

       1   0  -4

   1   0  -4  0

The remainder is zero, hence one factor is (x-1)

PART 3:

[tex]x^3-x^2-4x+4=(x^2-4)(x-1)\\\\x^3-x^2-4x+4=(x+2)(x-2)(x-1)[/tex]

PART 4:

[tex]f(x)=(x+2)(x-2)(x-1)\\\\=(x^2-4)(x-1)\\\\=x^3-4x-x^2+4\\\\=x^3-x^2-4x+4[/tex]


Related Questions

Given a = -3,b= 4 and e=-5, evaluate a+b+c

Answers

Answer:

-4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

a = -3,b= 4 and e=-5,

a+b+c

-3+4+-5

1 +-5

-4

May I have help on these two please, it’s for my sister?

Answers

#4.) 4
#5.) 3

Answers gotta be 20 characters long so ignore this part lol

Answer the question as an multiple choice.

Answers

Answer: i think its the first one 2/3

Answer:

2/3

Step-by-step explanation:

it starts off as 2:3 right? so the 3 is light soy sauce. if you want to turn the right soy sauce into 1 cup you have to divide 3 bye 3 which gives you one. then you also divide by 3 on the other side. that would be 2 divided by 3. 2 divided by 3 is the same as 2/3. so your answer is 2/3.

I need this answer rn can anyone help?

Answers

Answer:

Your answer should be, B.

Step-by-step explanation:

So, we can identify this as a transversal, which I will assume you already know what that is. When you have a transversal, you need to follow a certain set of rules, and don't worry, they're very simple.

Angle PSR is a vertical angle of angle OST, which automatically, according to your theorems, postulates, or properties, equal to each other. So with that in mind, you know that STN follows the same rules.

Additionally, where the lines intersect, each corresponding side MUST equal 180 degrees. So to find MTS, all you have to do is 180 minus 73, which gives you 107, completing that line.

Hopefully this isn't confusing!

2. In the diagram below, secants PT and PU have been drawn from exterior point P such that the four arcs
intercepted have the following ratio of measurements:
P
mRS : mST :MTU : mUR=1:4:4:3
R
(a) If mRS = x, then write an equation that could be used to solve for x
and find the value of x.
I
4
(b) State the measure of each of the four arcs.
mRS =
mST =
MTU
MUR =

Answers

Answer:

(a) x = 30°

(b) mRS =  30°

mST =  120°

mTU  = 120°

mUR = 90°

Step-by-step explanation:

(a) In the picture attached, the diagram is shown.

Given that m arc RS = x, from the ratios:

m arc ST = 4x

m arc TU = 4x

m arc UR = 3x

The addition of the four arcs must be equal to 360°, then:

x + 4x + 4x + 3x = 360°

12x = 360°

x = 360°/12 = 30°

(b) m arc RS = x = 30°

m arc ST = 4x = 4*30° = 120°

m arc TU = 4x = 4*30° = 120°

m arc UR = 3x = 3*30° = 90°

HELP PLZZZZZZ WITH THIS MATH PROBLEM!!!!!!!!!!!!!!!!

Answers

Answer:

I think it is A...

Step-by-step explanation:

None of the others really apply. Not the best at geometry in math. I had to look up, like, 12 words. I really hope this helped.

Peter, John and Mary share £60 in the ratio 3:5:4. How much does Mary receive?​

Answers

Mary receives 20

Look at the attached picture

hope it will help you

Good luck on your assignment

A circle has center (-2, 3) and radius 4 units. Which of the following is a point on
the circle?
A (-2,5)
B (-2,-1)
C (2,7)
D (-6, 7)

Answers

Answer:

B

Step-by-step explanation:

Which group of numbers is in order from smallest to largest? 0.34, 45%, , 0.8, 75% 27%, , 0.09 0.24, 37%,

Answers

Answer:

0.09, 0.24, 0.34, 27%, 37%, 45%, 75%, 0.8

Step-by-step explanation:

Answer: 0.34, 45%, 13/25

The person did not add the fractions in the question so you might think im wrong but i did the quiz and got it right:)

What’s the right answer?

Answers

I will give you the formula and teach you how to solve this. Let’s start with finding the area of both the right triangles.
The formula is, base x height / 2 = area
Triangle 1 - 2x8/2 = 16/2 = 8
Triangle 2 - 2x8/2 = 16/2 = 8
Rectangle - 8x3 = 24
Add them up: 24 + 8 + 8 = 40 square feet
I hope this wasn’t to confusing
40 square feet all you need to do for this shape is multiply the full top length and the side length :)

Assignment
Active
Converting Word Problems
1
1
Lindsay owns one-third the number of books that Destiny owns. Henry owns a fourth as many books as Destiny.
Together they own 57 books. If the equation -X+ x + x =57 models the scenario, how many books does Lindsay
3 4
own?
12
18
36
48

Answers

Answer:

12

step by step equation:

Lindsay owns 12 books.

Step-by-step explanation:

We can solve this question using a system of equations.

I am going to say that:

x is the number of books that Lindsay owns.

y is the nuber of books that Destiny owns.

z is the number of books that Henry owns.

Lindsay owns one-third the number of books that Destiny owns.

This means that:

, or

Henry owns a fourth as many books as Destiny.

This means that , or . Also, in function of x, we may have

Together they own 57 books.

This means that

We want to find x. So

Lindsay owns 12 books.

Indicate the number of solutions of each equation.
No Solutions
Exactly One Solution
Infinite Solutions
16a +1 = 11(a - 4)

Answers

Answer:

Exactly One Solution.

Step-by-step explanation:

16a +1 = 11(a - 4)

16a + 1 = 11a - 44

16a - 11a = -44 - 1

5a = -45

a = -9.


Talon Middle School received 219 prize packs. The school gave away f packs during school fundraisers. There were 42 packs passed out during pep rallies throughout the year. At the end of the year, the school had 54 prize packs left. How many packs were passed out during the fundraiser?

Answers

Answer:

123

Step-by-step explanation:

219 - 42 = 177 left

177 - f = 54

f = 177 - 54

f = 123 packs were passed out during the fundraiser

123

Step-by-step explanation:

219-42=177

177-54=123 or (f)

Check your work:

219-42=177

177-123=54

Therefore f=123 or 123 packs were passed out during the fundraiser.

Hope this helps! If you have any more questions or need further clarification on anything please feel free to comment down below or message me! Good luck!

the value of a baseball card after t years can be modeled by the function v(t)=10+2.5t find the value of the card after 20 years​

Answers

。☆✼★ ━━━━━━━━━━━━━━  ☾  

Simply substitute '20' as 't'

v(20) = 10 + 2.5(20)

value = 60

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

。☆✼★ ━━━━━━━━━━━━━━  ☾

Find the area of the polygon

Answers

Answer:

65

Step-by-step explanation:

You can split the polygon and find the area of the triangle STU and trapezoid SURO

Area of Trapezoid SURO: 49

Area of Triangle STU: 8*4/2= 16

49+16= 65

Answer:

65

Step-by-step explanation:

the area of the triangle is simply 8 times 4 divided by 2 which is 16

and the area of the trapezoid is 8+6/2 times 7 which is 49 and 49+16 is 65

What is the positive solution to the equation 0 = –x2 + 2x + 1? Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction –2 + StartRoot 2 EndRoot 2 – StartRoot 2 EndRoot 1 + StartRoot 2 EndRoot –1 + StartRoot 2 EndRoot

Answers

Answer:

See attached for a "Neat" quadratic formula.

a = -1

b = 2

c = 1

x = [-2 +- sqr root( 4 -4*-1*1)] / -2

x = [-2 +- sqr root( 4 -4*-1*1)] / -2

x = [-2 +- sqr root(8)] / -2

x1 = (-2 +2.8284271247)  / -2

x1 = .8284271247 / -2

x1 = -0.41421

x2 = (-2 -2.8284271247)  / -2

x2 = ( -4.8284271247)  / -2

x2 = 2.4142135624

So the equation has the positive solution of

2.4142135624

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Someone please helpp me quick awarding brainliest

Answers

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

1/3(1650 + 0.15c) = 1650/3 + 0.15c/3) = 550 + 0.05c

If limit as x approaches a of f of x equals two and limit as x approaches a of g of x equals four, then limit as x approaches a of the quantity three times f of x squared minus four times g of x equals negative four.

TRUE
FALSE

Answers

I think it's true but I'm not sure about that

The original price of a tractor was $55,000. The value decreases in value at a
steady rate of 11% per year. What will the tractor be worth in 8 years?
A) $21,651.24
B) $65,487.22
C) $45,591.35
D) $12,536.25

Answers

Answer:

A) $21,651.24

Step-by-step explanation:

x = p(1 - r)ⁿ

p = $55000

r = 11%  = 0.11

n = 8 years

x = $55000(1 - 0.11)⁸

= $55000ₓ0.89⁸

= $55000ₓ0.39365888057

= $21651.24

Solve the following equation by using the multiplicative inverse. Be sure to show all of your work.
5/6x = - 10

Answers

Answer:

x=-1/12

Step-by-step explanation:

hi got a question!
1.Write in algebraic form: m added to twice 7m?
2A half of a number added to 7 gives 19. What is the number?
thanks and please be quick!!​

Answers

Answer:

ok so keep it up kiddo keep asking questions and making us go nuts

Step-by-step explanation:

so ur answer is:

7m+2m24

What is the (y) intercept of a line given:y=x-6

Tom is buying topsoil for the flower bed shown below. One bag of topsoil covers 151515 square meters.

How many bags of topsoil does Tom need to cover his flower bed?

The Triangle has a base of 12 and a hight of 5

A. 2 bags
B. 3 bags
C. 4 bags
D. 5 bags

Answers

It is c, 4 assuming you meant one bag is 15
C but that’s just a guess

Please help i will give brainliest, thanks and more points

THESE QUESTIONS ARE FOR THE SHAPE IN THE PICTURE!

1) how many bases does it have

2) what is the figure called

Answers

Answer:

its called triangular pyramid

and it has one base

Step-by-step explanation:

1 base
Tranglar pyramid

Show your work to prove that the inverse of f(x) is g(x).
f(x)= x+10
-------
2
g(x)=6x-5

Answers

Answer: The inverse of f(x) is not g(x).

Step-by-step explanation:

Steps taken:

Swap x and y variablesSolve for yProve that the equations of f'(x) and g(x) are identical.

1.

[tex]f(x) = x + 10\\y = x + 10\\x = y + 10[/tex]

2.

[tex]x = y + 10\\y = x - 10[/tex]

The inverse of f(x) is x - 10, which does not match with g(x).

Maya can run 18 miles in 3 hours, and she can bike 18 miles in 2 hours.
What is Maya’s biking speed?

PLZ HELP IN A BIG RUSH PLZ PLZ PLZ

Answers

Answer:

Her speed is 9 miles per hour

Step-by-step explanation:

18 divided by 2= 9

so she can drive 9 miles in an hour

Chase is conducting A survey at school to see what their favorite subject is. He surveyed of 25 students from his math class. He found that 75% of the students in math what is their favorite subject. Is this a valid inference? Why or why not? Explain your answer to complete sentences.

Answers

Answer:

Not a valid inference.

Step-by-step explanation:

This is not a valid inference. This is because there may be a slight bias from the classmates he is asking, because, as the question read, he is in math class. Asking math class students if they like math or english more, may have a swayed opinion.

Answer:

No

Step-by-step explanation:

This is a biased survey, due to the fact he only asked his classmates in math. For a unbiased survey, everyone must have an equal chance of being picked.

2. Find the value of x. *
3(x + 2)
RE
24

Answers

Answer:

x=6

Step-by-step explanation:

3(x+2) = 24

Divide each side by 3

3/3(x+2) = 24/3

x+2 = 8

Subtract 2 from each side

x+2-2 = 8-2

x=6

3(6 + 2)
(6+2)=8
3(8)=24
24=24

Which triangle results from a reflection across the line x = 1?

Answers

Answer:

d

Step-by-step explanation:

Your savings account pays 2.5% interest per year. How much interest does the account pay per month.

Answers

Answer:

0.21%

Step-by-step explanation:

2.5/12=0.208 or 0.21

Based on the interest that your savings account pays per year, the interest paid per month is 0.21%.

How much interest is paid per month?

The interest paid per month can be found by dividing the yearly interest by the 12 months of the year.

Therefore, solving gives:

= Annual interest / 12 months

= 2.5% / 12

= 0.21%

In conclusion, this is 0.21%.

Find out more on savings interest at https://brainly.com/question/25787382.

#SPJ2

Math question for brainliest

Answers

Answer:

D

Step-by-step explanation:

because you are looking for an intercept and an intercept is a square equation which when divided by 4 takes a slope. WHich then D works to make the slope

Answer:

y - 9 = 1/2(x - 8)

Step-by-step explanation:

The point slope form of the equation of a line is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point

y - 9 = 1/2(x - 8)

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