What is the complete factorization of the polynomial function over the set of complex numbers?

f(x)=x3−5x2+4x−20



Enter your answer in the box.

Answers

Answer 1

Answer:

[tex]x^3-5x^2+4x-20=(x-5)(x+2\mathbf{i})(x-2\mathbf{i})[/tex]

Step-by-step explanation:

Factorization of polynomials

Factor:

[tex]f(x)=x^3-5x^2+4x-20[/tex]

There are several techniques to factor polynomials. We'll use algebraic manipulation and common factor:

Separate in groups:

[tex](x^3-5x^2)+(4x-20)[/tex]

Factor out 4 from 4x-20:

[tex]=(x^3-5x^2)+4(x-5)[/tex]

Factor out [tex]x^2[/tex] from [tex]x^3-5x^2[/tex]

[tex]=x^2(x-5)+4(x-5)[/tex]

Factor out x-5:

[tex]=(x-5)(x^2+4)[/tex]

The roots of

[tex]x^2+4=0[/tex]

Are two complex numbers:

[tex]x=2\mathbf{i}, x=-2\mathbf{i}[/tex]

The complete factorization is:

[tex]\boxed{x^3-5x^2+4x-20=(x-5)(x+2\mathbf{i})(x-2\mathbf{i})}[/tex]


Related Questions

How much cents are in 12 quarterS answer fast!!!!

Answers

Answer: 300 cents or 3 dollars

Step-by-step explanation: 12x25=300.

Answer:

300 CENTS

Step-by-step explanation:

hope this helps

Here are several recipes for sparkling lemonade. For each recipe
describe how many tablespoons of lemonade mix it takes per cup
of sparkling water,
Recipe 1: 4 tablespoons lemonade mix and 12 cups of sparkling
water
Recipe 2: 4 tablespoons of lemonade mix and 6 cups of sparkling
water
Recipe 3: 3 tablespoons of lemonade mix and 5 cups of sparkling
water
Recipe 4: 1 tablespoon os lemonade mix and 3 cups of sparkling
water

Answers

Answer:

Recipe 1: 1/2tbs of lemonade mix per cup of sparkling water

Recipe 2: 2/3tbs per cup

Recipe 3: 3/5tbs per cup

Recipe 4: 1/3tbs per cup

Step-by-step explanation:

To find the amount of lemonade mix per cup of sparkling water, we just need to divide the amount of lemonade mix in each recipe by its respective amount of sparkling water as this will give us the average amount per cup.

Recipe 1: 4 tbs lemonade mix, 12c sparkling water.

4/12 = 1/3, Recipe 1 requires 1/3 tablespoon per cup of sparkling water.

Recipe 2: 4tbs Lemonade, 6c water

4/6 = 2/3, Recipe 2 requires 2/3 tablespoon per cup of sparkling water.

Recipe 3: 3 tbs lemon, 5c water

Recipe 3 requires 3/5 tablespoon per cup of sparkling water.

Recipe 4: 1 tbs, 3c water

Recipe 4 requires 1/3 tablespoon per cup of sparkling water.

Hope this helped!

Write an expression to represent the submarine’s elevation after its final dive. Then simplify the expression to find its elevation

Answers

Answer:

-502.5 − 115 = -617.5

The submarine’s elevation after its final dive is -617.5 feet, or 617.5 feet below sea level.

Step-by-step explanation:

Plato answer

Answer:

63 1/4

Step-by-step explanation:

I did the edmentum

7(n+4)=21 what is n?

Answers

Answer:

-1

Step-by-step explanation:

divide both sides by 7 and you will get (n+4)=3

then subtract 4 on both sides and get n is equal to -1

Answer:

-1

Step-by-step explanation:

How much interest would $1,000,000 earn at 2% compound daily, in one day?

Answers

Answer:

$54.79 is the answer

Step-by-step explanation:

Write a linear function in slope intercept form given the slope of the equation is -4 and the y intercept is 6.

Answers

Answer:

6=-4x+b

Step-by-step explanation:

You plug in the numbers but the formula that you use is y=mx+b with x being the number you don't know

x3 = 0.008 what does the x equal

Answers

.2 because 2^3 is equal to 8. Which is 2*2*2=8.

Which expression is equivalent?

- 5(2x -3y +4)

Answers

Answer:

A

Step-by-step explanation:

Write one-page given the following scenario, determine if the salesman’s conjecture is logical? Why or why not? Is it true? Why or why not? Provide a counterexample that would disprove his hypothesis:

A car salesman sold 5 used cars to five different couples. He noticed that each couple was under 30 years old. The following day, he sold a new, luxury car to a couple in their 60’s. The salesman determined that only younger couples by used cars.

Answers

Answer:

His conjecture is not logical.

Step-by-step explanation:

If he sold a car to a couple above 30, how did he think only younger people bought cars? He is not logical.

HELP ME I NEED HELP EASY 10 POINTS

Answers

Answer:

X = 14

give me brainliest please

Step-by-step explanation:

3x + 29 = 7x - 27

3x + 56 = 7x

56 = 4x

x = 14

Turn this into numerical form -> one-half the sum of x and 12

Answers

Answer: 1/2(x+12)

Step-by-step explanation:

1. Write the equation of a line parallel to y = -2x + 10 that passes through point (2, 4). ​

Answers

Answer:

y - 4= -2(x - 2)

Step-by-step explanation:

(This answer is in point slope form, if you need the answer in a different form like slope intercept, you would have to distribute the negative 2 and bring the negative 4 to the right side.)

So, you know the line is parallel to the equation y= -2x + 10. We know that parallel lines must have the same slope, so the answer will have a slope of negative 2. Because they have given you a point that the line passes through, we are going to put the answer in point slope form. we know a point and we know the slope, hence it is called point-slope.

Point slope form is y - y₁ = m(x - x₁). The m stands for the slope, and the x₁ and y₁ is where you will plug in the x and y coordinates (2,4) .

So to plug in the numbers into point slope form it would be y - 4 = -2 (x - 2). hope this helped :)

Please help I’m not sure if I’m right

Answers

Answer:

C

Step-by-step explanation:

75.54*550=41,497.5

Question 4
Which of the following statements is true (read each carefully!):
.
The square root of 30 is between 6 and 7.
• The square root of 41 is between 5 and 6.
The square root of 14 is between 3 and 4.
• The square root of 27 is between 14 and 15.

Answers

The answer is : square root of 14 is between 3 and 4
√14= 3.74

Answer:

The square root of 14 is between 3 and 4.

Step-by-step explanation:

The answer would be that because the square root of 14 is  3.74165738677. HOPE THIS HELPS! CAN I HAVE BRAINLIEST?!

The other answer on the red box is 7.

Answers

Answer:

8

Step-by-step explanation:

that is an isosceles triangle. they have 2 sides that are the same

8*4 is 32+7 is 39

9*8 is 72-33 is 39

Are the following ratios equivalent? Explain.
2:10
6:60

Answers

Answer:

No

Step-by-step explanation:

it would 12:60

6x2=12

6x10=60

Answer:

they are not equivalent

Step-by-step explanation:

7 : 35

12 : 60

17 : 85

22 : 110

hear are ratios that are equivalent to 2:10

This equation shows how the total number of souvenirs Mark buys is related to the number of days he spends on vacation. s = d The variable d represents the number of days he spends on vacation, and the variable s represents the total number of souvenirs he buys. How many days will Mark have to spend on vacation before he will have bought a total of 12 souvenirs?

Answers

Answer:

12 days

Step-by-step explanation:

Given:

s = d

Where,

d = number of days he spends on vacation

s = total number of souvenirs he buys

How many days will Mark have to spend on vacation before he will have bought a total of 12 souvenirs?

s = 12

Since,

s = d

Then,

12 = d

Therefore, Mark will have to spend a total of 12 days on vacation before he will have bought a total of 12 souvenirs

Arisia puts $500.00 into a savings account with an annual simple interest rate of 4.5%.
Part A
How much interest does she earn per year?

Answers

Answer:

$22.50

Step-by-step explanation:

$500.00 × 0.045=22.50

Select the correct answer.
The formula for the voltage, V, of an electrical current is V = VPR, where Pis the power measured in watts and Ris the resistance measured
In ohms.
A toy train with a resistance of 10 ohms is powered by four 1.5-volt batteries. What is the power of the toy train?
OA. 0.225 watts
OB. 0.60 watts
Ос.
3.6 watts
OD
16.7 watts

Answers

I don't know the correct answer but I know its not 0.60 watts

Answer:

it is 3.6 watts

Step-by-step explanation:

there is no explanation but if needed proof i will try to post a picture of it

What is the slope of line p

Answers

U have to show us what line p looks like

2x+y=10 Find one non solution and solution. EXPAIN plz help i have a timed test ill make brainliest.

Answers

Answer:

x=20-y

y=20-x

Step-by-step explanation:

divide by 2 on both sides: x+y=20

to find x, subtract y:

x=20-y

to find y, subtract x:

y=20-x

nothing else can be done unless you know either y or x.

A movie theater has two rooms. Room A has 7 rows of seats with 21 seats in each row. Room B has four times as many seats as Room A. How many seats are there in both rooms?

Answers

Answer:

588

Step-by-step explanation:

Because 7x21=147 then you take 147x4 and that equals 588 seats

(x - 9) (x + 1)
Use F.O.I.L to expand

Answers

ok f.o.i.l

Farting.On.Iggy.Lucky

Answer:

x²-8x-9 i think?

Step-by-step explanation:

Logan used 12 centimeters of tape to wrap 4 presents. How much tape will Logan need in all if he had wrap 8 presents? Assume the relationship is directly proportional.

Answers

Answer:

24 centimeters

Step-by-step explanation:

slope=?

please help

Answers

Answer: It's 4

Step-by-step explanation: 12-8 is 4, 4-3 is 1

Chad sells custom T-shirts with five friends. They want to make enough money so that, after splitting the earnings evenly, each person earns 40

Answers

Answer: They earned 500 bucks in total

Answer:

They want to make 200 dollars

Step-by-step explanation:

40*5=200

Simplify√16 r6
A) 4r2
B) 4r3
C) 8r2
D) 8r3

Answers

Answer:

B) [tex]4r^{3}[/tex]

Step-by-step explanation:

[tex]\sqrt{16r^{6}}=\sqrt{4*4* r^{(3*2)}\\[/tex]

          [tex]=\sqrt{4^{2}*(r^{3})^{2}}\\\\=4*r^{3}\\\\=4r^{3}[/tex]

Answer:

B)  4r3

Step-by-step explanation:

Hope this helps.

HELP PLEASE!!! - Uranus is about 1.784109 miles from the Sun. About how far is Uranus from Mercury?

Answers

Answer:

About 1,749,638,696 miles.

Step-by-step explanation:

It might be incorrect so don't fully trust me.

please help asap!!! will give brainliest answer

Answers

Angle AOB and angle DOC are identical because they share 2 parallels considering it is a bisection.

Answer:

Angle AOB and angle DOC are identical because they share 2 parallels considering it is a bisection

Step-by-step explanation:

The United States Capitol is

located at (2, 4) on a coordinate grid. The White

House is located at (-10, 16) on the same coordinate

grid. Find two different points on a segment joining

the United States Capital and the White House such

that the ratio of the two shorter segments created by

each point is 1:3.

Answers

Answer:

The two different point on a segment joining the United States Capital and the White House such that the ratio of the shorter segments created by each is 1 : 3 are [tex]\vec C_{1} =(-1,7)[/tex] and [tex]\vec C_{2} = (-7,13)[/tex].

Step-by-step explanation:

At first we need to calculate the vector distance between [tex]A(x,y) = (2, 4)[/tex] and [tex]B(x,y) =(-10,16)[/tex] by following vectorial subtraction:

[tex]\overrightarrow{AB} = \vec B - \vec A[/tex] (Eq. 1)

Where:

[tex]\overrightarrow{AB}[/tex] - Vector distance between points A and B, dimensionless.

[tex]\vec A[/tex], [tex]\vec B[/tex] - Vector distance between each point and origin, dimensionless.

If we know that [tex]A(x,y) = (2, 4)[/tex] and [tex]B(x,y) =(-10,16)[/tex], then we have the following result:

[tex]\overrightarrow {AB} = (-10,16)-(2,4)[/tex]

[tex]\overrightarrow{AB} = (-10-2,16-4)[/tex]

[tex]\overrightarrow{AB} = (-12,12)[/tex]

Besides, we can find the location of any point inside the line segment by using the following vectorial equation:

[tex]\vec C = \vec A + r\cdot \overrightarrow{AB}[/tex] (Eq. 2)

Where:

[tex]r[/tex] - Segment factor, dimensionless.

[tex]\vec C[/tex] - Location of resulting point, dimensionless.

There are two different options for the location of resulting point: [tex]r_{1} = \frac{1}{4}[/tex] and [tex]r_{2} = \frac{3}{4}[/tex]. Now we proceed to find each option:

[tex]r_{1} = \frac{1}{4}[/tex]

[tex]\vec C_{1} = (2,4) +\frac{1}{4}\cdot (-12,12)[/tex]

[tex]\vec C_{1} = (2,4)+(-3,3)[/tex]

[tex]\vec C_{1} =(-1,7)[/tex]

[tex]r_{2} = \frac{3}{4}[/tex]

[tex]\vec C_{2} = (2,4) +\frac{3}{4}\cdot (-12,12)[/tex]

[tex]\vec C_{2} = (2,4) +(-9,9)[/tex]

[tex]\vec C_{2} = (-7,13)[/tex]

The two different point on a segment joining the United States Capital and the White House such that the ratio of the shorter segments created by each is 1 : 3 are [tex]\vec C_{1} =(-1,7)[/tex] and [tex]\vec C_{2} = (-7,13)[/tex].

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