what is the complete factorization of the polynomial below
[tex] {x}^{3} - {2x}^{2} + x - 2[/tex]


[tex]a. (x - 2)(x + i)(x - i)[/tex]
[tex]b.(x + 2)(x - i)(x - i)[/tex]
[tex]c.(x + 2)(x + i)(x - i)[/tex]
[tex]d.(x - 2)(x - i)(x - i)[/tex]

Answers

Answer 1

Answer:

[tex]a. \ (x-2)(x+i)(x-i)[/tex]

Step-by-step explanation:

First of all let's notice that [tex](x-i)(x-i)=(x-i)^2 = x^2+2xi-1 \in \mathbb{C}[/tex] while our original polynomial is real. So we can rule out the even options B and D. At this point, if the polynomial has a factor of [tex](x-\alpha)[/tex] it means tha [tex]\alpha[/tex] is a zero of the polynomial. Let's check both 2 (for option a) and -2 (for option c)

[tex]p(2)=2^3-2(2)^2+2-2= 8-8+2-2=0[/tex]

[tex]p(-2)= (-2)^3-2(-2)^2+(-2)-2=-8-8-2-2=-20[/tex]

At this point 2 is a zero, and our final factoring is a[tex](x-2)(x+i)(x-i)[/tex]


Related Questions

Kelly base 3328 cookies each year she bakes twice as many cookies in October then in the other much how many cookies does Kelly back in December

Answers

256 Cookies
There are 12 months and twice the amount of cookies in one month is equal to an extra month. So do 3328/13=256.

A bag contains 5 milk and 9 dark chocolates.
A sweet is selected at random.
What is the probability of choosing: P(milk)

Answers

Answer:

5/9

Step-by-step explanation:

The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width

Answers

Answer:

Length is 90yards and width is 60yards

Step-by-step explanation:

Perimeter= 2( length+width)

let the width be x

then the length will be 30 + x

300 = 2(30+x+x)

150 = 30 + 2x

120= 2x

x = 120/2

x = 60 yards

length= 30+x

= 30 + 60

= 90yards

(1) Mr. Jones finished correcting 6 out of 7 homework assignments. Miss Smith finished
correcting 83% of that week's homework assignments. Which teacher corrected a greater
percentage of her homework assignments?

Answers

Answer:

Mr. jones

Step-by-step explanation:

6/7 is 85.71% which is greater than 83%.

Help...................

Answers

Step-by-step explanation:

the surface area of that object consists of

2 triangles (one left, one right)

1 rectangle at the top

1 rectangle at the bottom

1 rectangle in the back

so, we need to calculate the area of each of these 5 areas and sum them up. that's it.

the area of such a triangle is

6×8/2 = 24 m²

we have 2 such triangles, so in total they are 48 m².

the rectangle at the top

10×12 = 120 m²

the rectangle at the bottom

12×8 = 96 m²

the rectangle in the back

12×6 = 72 m²

so the total surface area is

48 + 120 + 96 + 72 = 336 m²

Alistar is going to build fence around the outside of his garden

a) draw an accurate scale drawing of the garden using a ruler and compasses.use scale 1 cm to 2m

b) how long the fence be?

Answers

Answer:

32+[tex]\sqrt{200}[/tex]

Step-by-step explanation:

First - one side is 10m and other one is 16, so adding this 26m

Second-hypotenuse is sqrt of 10*10+10*10.

Third-  Remainder is 16-10 because  that is isosceles triangular.

hlep me pls daddddddddddddddddddddddddddddddddy

Answers

Answer:

The equation would be 2(n+3)-6. So A.

Step-by-step explanation:

It is asking you to subtract first and you cannot do that without  parentheses.

Answer:

First ONE

Step-by-step explanation:

First you are adding 3

n+3

then you mulitply by 2

so, its 2(n+3), you have to put in bracket because you want to do addition first

then you subtract everything by 6

its 2(n+3)-6

determine the intercepts of the line

Answers

Answer:

y- (0,2.5) x-(3.5,0)

Step-by-step explanation:

This is because the intercepts of a graph are the points at which a line intersects with a desired axis. So for the Y axis the inercept would be at 2.5 making the y intercept (0,2.5). The same concept is used on the X axis.

Obet has to wrap 25 gifts for the party. He has wrapped 10 gifts already. What percentage of the task has he done?
with solution please :D​

Answers

Answer:

40% is the solution 10÷25=0.40 which is well 40%

Help me solve this please

Answers

Step-by-step explanation:

8x + 4y <= 136

2x + y <= 34

trying (15, 9) :

2x + 7y <= 70

2×15 + 7×9 <= 70

30 + 63 <= 70

93 <= 70

that does not work. so, (15, 9) is not a valid point of f(x, y) and therefore also no maximum.

trying (0, 10) :

2×0 + 7×10 <= 70

70 <= 70

that is true.

2×0 + 10 <= 34

10 <= 34

also true.

so, (0, 10) is the correct answer option.

Solve for the unknown values.
95x
50y
X=
degrees
y =
degrees

Answers

Answer:

x=85 degrees, y=45 degrees

Step-by-step explanation:

solve for x first:

because there is a straight line (meaning that the angle is 180 degrees), the sum of x and 95 must be 180.

x+95=180 so solving for x would result in x=85 degrees (180-95)

then to solve for y:

the total sum of the interior angles of a triangle is 180 degrees.

so if you know x and the given 50, then to solve for y:

50+85(angle x)+y=180

then solve for y to get 45 degrees (180-(50+85))

The school counselor needs to meet with students who have more than three absences. Here is some of the data about the students. Who are the individuals in this data set?


- Students

- School counselors

- Homeroom teachers


What does this data set contain?


- 2 variables, 1 of which is quantitative

- 2 variables, 2 of which are quantitative

- 5 variables, 1 of which is quantitative

- 5 variables, 3 of which are quantitative

Answers

Answer:

The individuals in this data set are students. This data set contains 2 variables, 1 of which is quantitative.

Step-by-step explanation:

Individuals are the people or things described by a data set.

Variables are characteristics of the individuals that we measure or observe.

Categorical variables take on values that are labels or categories, and quantitative variables take on numerical variables.

The individuals described by this data set are students.

The characteristics listed--homeroom teacher and absences--describe each of the students, not teachers or counselors.

One of the variables--absences--is quantitative.

The individuals in this data set are students. This data set contains 2 variables, 1 of which is quantitative.

What is a dataset?

A data set is a set of information. A data set corresponds to one or more database tables in the case of tabular data.

Individuals are the people or things described by a data set.Variables are characteristics of the individuals that we measure or observe.

Categorical variables take on values that are labels or categories, and quantitative variables take on numerical variables. The individuals described by this data set are students.

The characteristics listed--homeroom teacher and absences--describe each of the students, not teachers or counsellors. One of the variables--absences--is quantitative.

Therefore the individuals in this data set are students. This data set contains 2 variables, 1 of which is quantitative.

To know more about datasets follow

https://brainly.com/question/251701

#SPJ2

Pure acid is to be added to a 10% acid solution to obtain 90L of 81% solution. What amounts of each should be used?
How many liters of 100% pure acid should be used to make the solution?

Answers

Answer:

Step-by-step explanation:

let X be the quantity of 100% acid

let Y be the quantity of  10% acid

X + Y = 90

Y = 90 - X

         X(100) + Y(10) = 90(81)

X(100) + (90 - X)(10) = 90(81)

   100X + 900 - 10X = 7290

                         90X = 6390

                              X = 71 L

For f(x) = 2(6)*, find y when x=2.
f(2)=

Answers

Answer:

I believe it is f(2) = 12

Step-by-step explanation:

I don't know if the * symbol is supposed to be an x but if it is, it would be 12x instead of 12.

A birthday cake was cut into equal pieces, and 10 pieces were eaten. The
fraction below shows how much cake was left over. According to the fraction,
into how many pieces was the cake cut?
1
11
A. 1
B. 10
C. 21
O D. 11
TO

Answers

The answer is D, 11.

A tiled floor measures 1 ⅔ by 2 ⅔ feet. What is the area of the floor?

Answers

let's firstly convert the mixed fractions to improper fractions and then multiply.

[tex]\stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}}~\hfill \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{3}\cdot \cfrac{8}{3}\implies \cfrac{40}{9}\implies 4\frac{4}{9}[/tex]

Compare the linear equation 2x-y=4 to the function graphed below.

Answers

Answer:

The answer is be the intercept

Expressions equivalent to 8 to the negative 2 power times 3 to the negative 2 power

Answers

Answer:

0.0007361111111111111+0.001;

0.0027361111111111111-0.001;

1.0017361111111111111-1;

Step-by-step explanation:

you calculate 8^(-2)*3^(-2) that gives you 0.0017361111111111111 and then you add 1 anywhere you want and then say -1 where you put that +1 and that's all

Christina says the graph for the inequality r < -5 will be the same as the graph for the inequality -5 > r. Do you agree or disagree? Justify your reasoning. (Explain) HELP

Answers

Answer:

Agree

Step-by-step explanation:

Just copy and paste (without quotations): "I agree because r < -5 is just a flipped inequality of -5 > r. In other words, 'r is less than -5' is the same as '-5 is greater than r'."

PLEASE HELP WILL MARK BRAINIEST!!!!!!

Answers

B is the answer as when you draw angle bisector you draw arcs that intersect at the bisector

GEOMETRY MULTIPLE CHOICE

Answers

Answer:

E seems to be the only one that is true

Step-by-step explanation:

its just asking you basically which ones are true based on the info they already give you

I do believe the Answer is E

24. Solve for x: 3x - 2(x - 4) = 5(2x + 4) -3

Answers

x=-1

3x-2x+8=10x+20-3

x+8=10x+17

-9x=9

x=-1

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

[tex]x-2\left(x-4\right)=5\left(2x+4\right)-3[/tex]

[tex]-2\left(x-4\right)\\\mathrm{Distribute}\\-2x+8[/tex]

[tex]3x-2x+8=5\left(2x+4\right)-3[/tex]

[tex]\mathrm{Combine\: like\: terms}[/tex]

[tex]x+8=5\left(2x+4\right)-3[/tex]

[tex]\left(2x+4\right)-3\\\mathrm{Distribute}\\10x+20-3\\10x+17[/tex]

[tex]x+8=10x+17[/tex]

[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]

[tex]x+8-8=10x+17-8[/tex]

[tex]x=10x+9[/tex]

[tex]\mathrm{Subtract\:}10x\mathrm{\:from\:both\:sides}[/tex]

[tex]x-10x=10x+9-10x[/tex]

[tex]-9x=9[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-9[/tex]

[tex]\frac{-9x}{-9}=\frac{9}{-9}[/tex]

[tex]\bold{x=-1}[/tex]

Which of the following is a solution of x2+5x=-2
A.5+ √33
———-
2
B. 5+ √17
———-
2

C.-5+ √33
———-
2
D. 5+ √17
———-
2

Answers

x^2 + 5x = -2

x^2 + 5x + 2 = 0

We need to use the quadratic formula.

In the formula, a = 1, b = 5 and c = 2.

See picture for quadratic formula. Plug in the value for a, b, and c into the formula and do the math.

How can you solve problems involving percents?

Answers

Step-by-step explanation:

To solve percent problems, you can use the equation, Percent · Base = Amount, and solve for the unknown numbers. Or, you can set up the proportion, Percent = , where the percent is a ratio of a number to 100.

Answer:

Base = Amount, and solve for the unknown numbers.Step-by-step explanation:

Or, you can set up the proportion, Percent = , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion.

Image attached giving 25 points please help

Answers

Answer:

Rational

Step-by-step explanation:

It isnt whole because its a decimal,

It isnt an Integer because its a decimal

It isnt natural because its a decimal

Meaning it can only be rational

What is the sum of 6/7 and 1/2?

Answers

Answer: [tex]\frac{19}{14}[/tex] in improper form and [tex]1\frac{5}{14}[/tex] in mixed fraction form.

Step-by-step explanation: [tex]\frac{6}{7}[/tex] + [tex]\frac{1}{2}[/tex] = ? First you have to find the LCM (Least Common Multiple) of 7 and 2; also known as the LCD (Least Common Denominator). The LCM of 7 and 2 is 14 so you have to multiply both of the fractions by the number that equals 14, remember to multiply it for the numerator too. [tex]\frac{6}{7}[/tex] x [tex]\frac{2}{2}[/tex] = [tex]\frac{12}{14}[/tex] Then [tex]\frac{1}{2}[/tex] x [tex]\frac{7}{7}[/tex] = [tex]\frac{7}{14}[/tex] Now you add [tex]\frac{12}{14}[/tex] and [tex]\frac{7}{14}[/tex] together. You leave the denominator as 14 because you found the LCD of 7 and 2 already, so you add 12 and 7 together which gives you 19. The answer would be [tex]\frac{19}{14}[/tex] in improper fraction form and [tex]1\frac{5}{14}[/tex] in mixed fraction form.

The sum of the fraction 6/7 and 1/2 is 19/14

How to add fractions

Given:

sum of 6/7 and 1/2

Sum means addition(+)

= 6/7 + 1/2

The least common denominator is 7 × 2 = 14

= 6/7 + 1/2

= (12+7) / 14

= 19/14

Therefore, the sum of 6/7 and 1/2 is 19/14

Learn more about fraction:

https://brainly.com/question/11562149

20points
Which represents the restrictions on the radical inequality

Answers

The second i think you did good

Answer:

The answer is 2x>0 is the final answer. The last one.

Step-by-step explanation:

It is greater.

Help me(((((((please

Answers

Answer:

I do not know English

Step-by-step explanation:

<3333

An athlete runs 1, miles in 7 minutes. At this rate, how long does it take the athlete to run 1 mile?
174
o minute
0.6 minutes
O 74 minutes
O 9 minutes

Answers

Answer:

My closest calculation is 74 minutes

Step-by-step explanation:

08 : 59.52

min : sec

Speed

0.1112 miles per minute

=

6.67 miles per hour

Find m< FED Im
giving this question 20 points

Answers

Answer:

180° - (61° + 61°) = 58°

Step-by-step explanation:

we can see that two sides of the angle are equilateral making it equiangular therefore the other angle is 61° and solve for <FED

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