If (x+5) is one of the factors of the polynomial x3 + x2 - 32x - 60, find the remaining roots.

Answers

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:

x = 5

x = 2

x = -6

Step-by-step explanation:

Use synthetic division to determine whether x – 4 is a factor of:

–2x5 + 6x4 + 10x3 – 6x2 – 9x + 4

For x – 4 to be a factor, you must have x = 4 as a zero. Using this information, I'll do the synthetic division with x = 4 as the test zero on the left:

completed division

Since the remainder is zero, then x = 4 is indeed a zero of –2x5 + 6x4 + 10x3 – 6x2 – 9x + 4, so:

Yes, x – 4 is a factor of –2x5 + 6x4 + 10x3 – 6x2 – 9x + 4

Find all the factors of 15x4 + x3 – 52x2 + 20x + 16 by using synthetic division.

Remember that, if x = a is a zero, then x – a is a factor. So use the Rational Roots Test (and maybe a quick graph) to find a good value to test for a zero (x-intercept). I'll try x = 1:

completed division

This division gives a zero remainder, so x = 1 must be a zero, which means that  x – 1 is a factor. Since I divided a linear factor (namely, x – 1) out of the original polynomial, then my result has to be a cubic: 15x3 + 16x2 – 36x – 16. So I need to find another zero before I can apply the Quadratic Formula. I'll try x = –2:

completed division

Since I got a zero remainder, then x = –2 is a zero, so x + 2 is a factor. Plus, I'm now down to a quadratic, 15x2 – 14x – 8, which happens to factor as:

(3x – 4)(5x + 2)

Then the fully-factored form of the original polynomial is:

15x4 + x3 – 52x2 + 20x + 16

= (x – 1)(x + 2)(3x – 4)(5x + 2)

Given that  x = -3 + sqrt(11)   is a zero of x4 + 6x3 – 7x2 – 30x + 10, fully solve the

equation x4 + 6x3 – 7x2 – 30x + 10 = 0.

Since they have given me one of the zeroes, I'll use synthetic division to divide it out:

completed division

(You will probably want to use scratch paper for the computations required when manipulating the radical root.) Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

Since you only get these square-root answers by using the Quadratic Formula, and since the square-root part of the Formula is preceded by a "plus-minus" sign, then these square-root answers must always come in pairs. Thus, if x = -3 + sqrt(11) is a root, then so also must x = -3 - sqrt(11) be a root. So my next step is to divide by x = -3 - sqrt(11):

completed division

I had started with a fourth-power polynomial. After the first division, I was left with a cubic (with very nasty coefficients!). After the second division, I'm now down to a quadratic (x2 + 0x – 5, or just x2 – 5), which I know how to solve:

x = +/- sqrt(5)

Then the full solution is:

x = -3 +/- sqrt(11), +/- sqrt(5)

If you have studied complex numbers, then you may see a problem of the following type.

Given that 2 – i is a zero of x5 – 6x4 + 11x3 – x2 – 14x + 5, fully solve the

equation  x5 – 6x4 + 11x3 – x2 – 14x + 5 = 0.

They have given us a zero, so I'll use synthetic division and divide out 2 – i:

completed division

(You will probably want to use scratch paper for the computations required when doing complex division.)

Recall that, to arrive at a zero of 2 – i, they must have used the Quadratic Formula, which always spits out complex answers in pairs. That is, you get the imaginary part (the part with the "i") from having a negative inside the "plus or minus square-root of" part of the Formula. This means that, since 2 – i is a zero, then 2 + i must also be a zero.  So I'll divide by 2 + i:

completed division

This leaves me with a cubic, so I'll need to find another zero on my own. (That is, I can't apply the Quadratic Formula yet.) I can use the Rational Roots Test to help find potential zeroes, and a quick graph of x3 – 2x2 – 2x + 1 can help. I will try x = –1:

completed division

Now I'm down to a quadratic (x2 – 3x + 1, which happens not to factor), so I'll apply the Quadratic Formula to get:

x = (3 +/- sqrt(5))/2

Then all the zeroes of x5 – 6x4 + 11x3 – x2 – 14x + 5 are given by:

x = 2 - i, 2 + i, (3 - sqrt(5))/2, (3 + sqrt(5))/2, -1


Related Questions

Chin bought 12 pounds of apples for $6. Use the ratio table to find the cost of buying 3 pounds of apples. *

Answers

Answer: The answer should be 1.5.

Step-by-step explanation:

$6 divided by 12 is .5... Multiply .5 by 3, seeing as 1 pound = $.5

Answer:

$.5

Step-by-step explanation:

hope this helps y'all

can someone help my sister with her module? she in 6th,and i am way to dumb to know how to help her (i gib link)

Answers

Answer:

Sure!

Step-by-step explanation:

Brenda wants to buy a phone case that costs $35. It is on sale for 20% off. What would be the sales price? What are we finding?

A) part
B) whole
C) percent

Answers

Answer:

A

Step-by-step explanation:

I don’t understand help me plz hard

Answers

Answer:

-2 1/2 is the correct answer

I hope this helps! If it is correct please mark brainliest answer, thank you!

Stay safe, God bless and happy studying!

I need help with this, Its geometry

Answers

Answer:

Step-by-step explanation:

x + 17 + 6x + 10 + 4x - 34 = 180

11x + 27 - 34 = 180

11x - 7 = 180

11x = 187

x = 17

x + 17 = 17 + 17 =34

6(17)+10 = 102 +  10 = 112

4(17) - 34 = 68 - 34 = 34

Answer is D

Yesterday, the temperature in a city dropped from 9°C to –9°C, as shown below.



The expression 9 + (–18) represents the final temperature. Which of the following is an equivalent way to describe this temperature?

|–18| degrees in a negative direction from 9 degrees

|–18| degrees in a positive direction from 9 degrees

|–9| degrees in a negative direction from 9 degrees

|–9| degrees in a positive direction from 9 degrees

Answers

Answer:

I belive the correct answer might be (A)

Solve the problem. Show your work

Answers

Answer:

D correct

Step-by-step explanation:

Determine the intercepts of the line.
y = 80 - 18

Answers

Answer:

Step-by-step explanation:

This equation is in slop-intercept form. This means that the y-int is in the equation, it will always be the constant, so y is -18.

To find x, set y to 0.

0 = 8x - 18

18 = 8x

18/8 = x

9/4 = x

What is the value for angle 2?

I need help

Answers

Answer:

120

Step-by-step explanation:

all complementary angles should add up to 180 degrees

Answer:

the value of 2 is 60

Step-by-step explanation:

Wait So Do You Multiply Fractions Like Lets Say The Problem Was 2 x 9
8 1 Right So Do I Multiply 9x1 Then 1x2 Then 8x9 Then 8x2?
I Learned How To Do Them A While Ago But Forgot.

Answers

Answer:

can you take a photo of the question you're asking for? I can answer it, but your question was kinda worded funny so I don't rest understand what you mean. I'm good at fractions, so I will be happy to help:)

A rectangular garden has an area of 35 square miles. If its length is 78 miles, what is its width?
Input your answer as a fraction.

Answers

Answer:

9/20 mi

Step-by-step explanation:

A= b*hFill in the Values

35 = 78 * h

3. divide 35 by 78 = 0.44871794871

4. round that to .45

5. To make a fraction, put it over 100

45/100

7. Simplify fraction

9/20

Diyva has 70 rocks.she donates half of the rocks to a science center. then she collects 3 rocks on each of her nature hikes

Answers

Answer:

What are you asking here? This is more like a statement.

Step-by-step explanation:

Answer:

I'm just going to assume that your trying to figure out how many rocks she has left, in which case the answer would be 38.

Please answer correctly !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

x=57 degree

Step-by-step explanation:

Answer:

x=57

Step-by-step explanation:

(x-5) + (2x+4) = 180

get all xs on the same side non xs on other side till you get

3x=171

then divide 171 by 3

x = 57

Need help with geometry question

Answers

Answer:

B. 66

Step-by-step explanation:

idk how to explain it without repeating what it says in the answer

Answer:

The answer is:

B) 66 degrees

Step-by-step explanation:

Since the triangle is an isosceles triangle, angle C is the same as angle B.

57 + 57 = 114

Since you know two of the three angles, and you know that a triangle's angles must equal 180 degrees...

180 - 114 = 66

Angle A must equal 66 degrees for the triangle to equal 180 degrees.

I hoped this helped you! If it did, please consider rating and pressing the 'Thanks' button. Have great day!

WILL GIVE BRAINLIEST
On a field trip, there are 8 adults and 24 students. What is the ratio of students to the total number of people on the field trip?

8 to 24
3 to 4
1 to 4
32 to 24

Answers

Answer:

3:4

Step-by-step explanation:

24 students : 32 people total

Divide both sides by 8

Answer: 3 to 4

this is correct, verified it myself B)

It also detects if you are right or wrong

Answers

Answer:

50

Step-by-step explanation:

all your doing is dividing 100 by 20 and u get 50

Answer: 15. A. Proportional 16. B. 50 mph

Step-by-step explanation: The price and the number of apples are proportional based on the info you have given us. And B. 50 is correct because 100 miles in 2 hours is 100/2 which equals 50/1 so the unit rate would be B. 50 mph.

What is the slope of this line?

Enter your answer as a fraction in simplest term in the box.

Answers

Answer:

1/4

Step-by-step explanation:

y2-y1/x2-x1

6-5/ 0 - -4.... since it's two subtract signs facing each other you turn it into a +..... 1 /4

Answer:

1/4

Step-by-step explanation:

y2-y1/x2-x1

6-5/ 0 - -4.... since it's two subtract signs facing each other you turn it into a +..... 1 /4

WILL GIVE BRAINLIEST EASY

drag and drop correct answers

Answers

Answer:

X- int: -3,0 and 1,0

Y- int: -3, 0

Domain: -inf to +inf

Range:+in to -4

Minimum Value : -4, 1

PLEASE HELP ASAP
Factor 3x+6y-9z

Answers

I’m not sure what the answer is so better I don’t say I don’t want you to get it wrong

On a scavenger hunt, you find 16 out of 25 objects. Write "16 out of 25" as a fraction, a decimal, and a percent.
Fraction:
Decimal:
Percent:
I need help ASAP

Answers

Answer:

Fraction: 16/25 Decimal: 6.25 Percent: 6%

Step-by-step explanation:

I am 99.99% sure this is right.. I hope it helps you.

The statements "16 out of 25" written in fractional, decimal, and percent form are 16/25, 0.64, and 64% respectively.

What is a fraction?

A fraction is a part of the whole represented by a/b, where a and b are any integers.

The Given statement is "16 out of 25".

The statement in mathematical form is:

16/25 (Fraction)

= 0.64 (Decimal)

= 64% (percent)

Hence, the statements "16 out of 25" written in fractional, decimal, and percent form are 16/25, 0.64, and 64% respectively.

Learn more on fractions here:

brainly.com/question/10354322

#SPJ2

An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is $24.6, and the standard deviation is known to be $7.9. How large of a sample would be required in order to estimate the mean per capita income at the 80% level of confidence with an error of at most $0.56? Round your answer up to the next integer.

Answers

Answer:

327

Step-by-step explanation:

Calculation for How large of a sample would be required in order to estimate the mean per capita income

First step is to find z 80% confidence level

At 80% confidence level the z will be:

α/2 = 1 - 80% = 1 - 0.80 = 0.20

α/2= 0.20 / 2 = 0.01

Zα/2= Z0.01= 1.28 from z table

Now let calculate the Sample size using this formula

Sample size = n= [( Zα/2* σ ) / E]^2

Let plug in the formula

n = (1.28*7.9/0.56)^2

n= 326.06

n=327 (Approximately)

Therefore How large of a sample would be required in order to estimate the mean per capita income will be 327

Which set of numbers does NOT describe the side
lengths of a right triangle?
a. 3, 4, 5
b. 5, 12, 13
c. 6, 14, 17
d. 7, 24, 25
4

Answers

Answer:

The answer is C

Step-by-step explanation:

You have to do the Pythagorean Theorem.

A. you get 25=25

B. you get 169=169

C. you get 232=289

D. you get 625=625

please i need this quick , it’s so confusing

Answers

i think its A : 25 B : 81 C: 49

Dierections:Factor out the GCF from the following.Make sure your answer is factored completely by taking out any common numbers and or variables

Answers

Answer:

21

Step-by-step explanation:

your mom

Need help!! How do I figure out the question.

Answers

Answer:

its the second one lol its just asking you to pick the one less than a and a is 0.11 so it would be 0.0019

Step-by-step explanation:

Aiman has 6 pizzas to share at a party. If each person will eat 3/8 of a pizza, how many people can share the pizzas?
A 48 people
B 16 people
C 2 people
D 6 people

Answers

Answer:

The amswer is B, 16 people.

4 x 7/8 Pls I need help my mom is yelling at me

Answers

Answer:

3.5

Step-by-step explanation:

Answer:

7/2 or 3 1/2

Step-by-step explanation:

4 * 7/8 = 4/1 * 7/8 = 28/8 = 7/2 = 3 1/2

best estimate for 7/8-6/11

Answers

Ummm we are allll gonna be dead cause Biden be da president

Answer:

WE ARE GONNA DIE

Step-by-step explanation:

BECAUSE BIDEN IS THE PRESIDENT AND DONALD TRUMP IS NOT. >.< I DONT LIKE BIDEN!!!!

what is the slope of the line passing through the points (0,-5) and (4,2)

Answers

Answer: 7/4.

Step-by-step explanation: To find the slope of a line, one must use the formula (y2-y1)/(x2-x1). In this case y2 is 2, y1 is -5, x2 is 4, and x1 is 0. We can plug this into the equation to get 7/4.

a bowl contains 15 gra

Answers

Answer: hi

Step-by-step explanation:

Answer:

And, so...

What about the 15 grams?

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