The polynomial of degree 5, P(2), has leading coefficient 1, has roots of multiplicity 2 at x = 4 and
x = 0, and a root of multiplicity 1 at 3 3.
Find a possible formula for P(x).
P(x)

Answers

Answer 1

Answer:

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

Step-by-step explanation:

Each root corresponds to a linear factor, so we can write:

[tex]P(x)=x^{2} (x-1)^{2} (x+3)\\=x^{2} (x^{2} -2x+1(x+3)\\\\=x^{5} +x^{4} -5x^{3} +3x^{2}[/tex]

Any polynomial with these zeros and at least these multiplicities will be a multiple (scalar or polynomial) of this [tex]P(x)[/tex]

Footnote

Strictly speaking, a value of [tex]x[/tex]  that results in [tex]P(x)=0[/tex] is called a root of  

[tex]P(x)=0[/tex] or a zero of [tex]P(x)[/tex] . So the question should really have spoken about the zeros of [tex]P(x)[/tex]  or about the roots of [tex]P(x)=0[/tex]


Related Questions

HELP PLSSS THIS IS HARD SOMEONEEE

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Answer:

2 option

Step-by-step explanation:

mark me as brainliest

Answer:

Oh Im so Sorry But U Can Do It

What is the square root of 18 plus the square root of 2? And is it rational or irrational?

Answers

The answer is (rounded to the nearest tenth) about 5.7 and since neither 18 or 2 have a perfect square, so this is irrational.

if you purchesd a $49.00 gift and you use a 20% off coupon how much do you spend

Answers

Answer:

$39.20

Step-by-step explanation:

$49 * (1-.2) = $39.20

Schumer Box How To Read The Fine Print

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Answer:

what'd you mean?

Step-by-step explanation:

What is the slope of a line that is parallel to the given line

Answers

slope(initial): -3/2

the slope of the parallel line would also be: -3/2

Hope this helps!!

Answer:

The slope of the parallel line is -3/2

Step-by-step explanation:

Calculate the slope using rise over run then simplify.

-6/4 , -3/2

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plz no silly answers

Answers

Answer:

64, -64, -64

-27, 27, 27

Step-by-step explanation:

If x = 4,

x³ = 4³ = 64

-x³ = -4³ = -64

(-x)³ = (-4)³ = -64

If x = -3,

x³ = -3³ = -27

-x³ = -(-3)³ = 27

(-x)³ = (-(-3))³ = 27

HELPPP PLEASE WILL MARK BRANLIEST

Answers

Answer:

The answer is 6

Step-by-step explanation:

Why is it 6? because surface means like the total faces it has.

Helppp I will give u 100 if you give me a good answer

Answers

Answer: it allows you to see both sets of data more clearly and compare them rather than having them on two different charts.

Step-by-step explanation:

Help please.............................................................

Answers

Answer:

the third one

Step-by-step explanation:

The line passes through the point

-The slope of the line is 4

- y int is -6

pls help
Which of the sets of ordered pairs represents a function? (5 points)

A = {(3, −5), (4, 6), (−3, 9), (2, 7)}
B = {(2, 4), (−1, −7), (5, 6), (4, 3)}

Answers

Answer: both

Unless you mistyped the first number and it’s actually -3 instead of 3 than b is the answer.

To see if they make a function you can graph all the coordinates and do the line test. Or you can look at all the numbers and see if any of the ordered pair have repeating x values. If they do, it’s not a function.

Remember, it’s (x,y) and if any X values repeat, it’s NOT a function

What is the common ratio of 4,-5,-14,-23,-32

Answers

Answer:

-9!!!

Step-by-step explanation:

4 - 9 = -5

-5 - 9 = -14

-14 - 9 =  -23

-23 - 9 = -32

Brainliest me plzzz


Why might you write the equation in
point-slope form instead of slope-intercept
form?

Answers

Step-by-step explanation:

Slope-intercept form is useful when we know the y- intercept of a line. However, we are not always given this information. When we know the slope and one point which is not the y-intercept, we can write the equation in point-slope form.

I hope this will help you out!

The equation of a line whose slope is 'm' and which passes through a point (x1, y1) is found using the point slope form.

We need to check why might we write the equation in point-slope form instead of slope-intercept form.

What is point-slope form?

Point slope form is used to represent a straight line using its slope and a point on the line. That means, the equation of a line whose slope is 'm' and which passes through a point (x1, y1) is found using the point slope form. Different forms can be used to express the equation of a straight line. One of them is point slope form. The equation of the point slope form is: y - y1 = m(x - x1)

where, (x, y) is a random point on the line and m is the slope of the line.

The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as: y = mx + b.

We use point-slope form with one coordinate and slope.

Therefore, the equation of a line whose slope is 'm' and which passes through a point (x1, y1) is found using the point slope form.

To learn more about the point slope form visit:

https://brainly.com/question/24436844.

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Eirxxjdjenendhdjcjcjfjfjirrorj

Answers

Answer:

hsoabajakahaknanaKambaKla

If f(x) = 2x^2 - 3 and g(x) = x + 1, find g(f(x)).

Group of answer choices

2x^2 - 2

2(x+1)^2 - 3

2x^2 + 2

2x^3 + 2x^2 - 3x - 3

Answers

Answer:

g(

x

2

3

)

=

2

x

2

7

Step-by-step explanation:

brainliest

Express the inequality using interval notation. PLEASE HELP DUE TONIGHT WILL GIVE BRAINLIEST

Answers

Answer:

Convert the inequality to interval notation.

(-∞, 0) ∪ (7, ∞)

What does the transformation f(x)↦f(x)+5 do to the graph of f(x)?

Answers

Answer:

Moves it up 5 units

Step-by-step explanation:

The +5 outside of any parenthesis on a graph moves it up.

I really need help for this I need explanations of this please I need to submit right now please help

Answers

No because a rigid motion does not change the area (shape or/and size). It would be a non-rigid motion because is B was to be on planted on A it would overlap A.

Amy has $70.00 and Alice has $9.52. How much money do they have
together?

Answers

Answer:

Together they have $79.52

Which of the following is a correct conversation factor?

Answers

Answer:

B

Step-by-step explanation:

1000mm=1m

‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌

ANSWER:

1,000mm = 1m

B

{x: x belongs to N and (x-1)(x-2) = 0}, finite set or infinite set?

Answers

Answer: Finite Set

Explanation:

We have a set of x values such that (x-1)(x-2) = 0. Breaking that down leads to either x-1 = 0 or x-2 = 0 through the zero product property. Solving each of those equations gets us x = 1 and x = 2 as the two items in this set.

So the original set your teacher gave you turns into the roster form {1,2}. There are two items in this set and we can see it's a finite set since it does not go on forever. Note that everything in this set is a natural number.

Guys pls help me!!!!!!!

Answers

Answer:

64 degrees

Step-by-step explanation:

since x is corresponding to 64, they are congruent.

Answer:

x = 64

Step-by-step explanation:

x and 64° are corresponding angles and are congruent , then

x = 64

WILL GIVE BRAINLIEST. a. determine a rule for the table B. complete the table. for input for 4 and n.

Answers

Answer:

WHAT TYPE OF MATH LIKE WHAT LESSON

Step-by-step explanation:

I’m completely confused on this, but I’ll take a guess

|-The output for 4 is 10
|-the output for the three dots is 13
|-the output for N is 16

If you look at the output for the previous numbers, 1, 4, and 7- you notice that 1+3=4 and 4+3=7, assuming this may be a rule, you can add 3 to 7 which gets you 10, continuing on 10+3=13 and 13+3=16. Next for the input try to see what the input and output have in common. 1 and 1, 2 and 4 and 3 and 7. 1+0=1 2+2=4 3+3=6(+1) =7 4+4=8 (+2)=10 (continue this for the three dots) 5+5=10 (+3)=13. Because of this the input for the three dots would be 5. For N, it would be 6+6=12(+4)=16, so the input for N would be 6.

(Once again I’m not completely sure how this works, and it may be a lot more complex than this (I’m so so so so so sorry if it’s wrong )

Help stuck on this question

Answers

Answer:

Find the slope of the original line and use the point-slope formula: y−y1=m(x−x1 )

to find the line parallel to -> y = 6/7 x −2.

A: y = 6/ 7x−7

standard deviation of 0.116 minute. The winning car that year, driven by Tammy, finished in 110.49 minutes. Find their respective Z-scores. Who had the more convincing victory?
The mean finish time for a yearly amateur auto race was 185.24 minutes with a standard deviation of 0.397 minute. The winning car, driven by Ron, finished in 183.98 minutes. The previous year's race had a mean finishing time of 110.8 with a
Ron had a finish time with a 2-score of
Tammy had a finish time with a 2-score of
(Round to two decimal places as needed.)
Which driver had a more convincing victory?
O A. Ron had a more convincing victory because of a higher Z-score.
OB. Tammy a more convincing victory because of a lower Z-score.
OC. Tammy a more convincing victory because of a higher Z-score.
OD. Ron had a more convincing victory because of a lower Z-score.

Answers

The answer should be B

a homework assignment included 40 multiple choice questions Sabrina completed 65% of her assignment in David completed 4/5 of his assignment how many more questions did David complete compared to sabrina?​

Answers

Answer:

6 or -6

Step-by-step explanation:

65% of 40=264/5 of 40=3232-26=6(or if you start with 26)26-32=-6
6 or -6 :))) Have a great day

a board that is 4 1/2 feet long weighs 7 1/5 pounds how much would one foot of the board weigh? write your answer as a mixed number

DESPERATE PLEASE HELP WILL AWARD BRAINLIEST

Answers

Answer: 1 foot = 5/3 or 1.6666 pounds

Step-by-step explanation: to get 4 1/2 feet to one foot, you divide by 4 1/2. in this equation, 4 1/2 ft= 7 1/2 pounds. if you divide one side by 4 1/2, you also have to do the same to the other side. therefore you do 7 1/2 divided by 4 1/2 which will give you 1.6666 or 5/3.

1 foot= 5/3 pounds

Find the equation of the linear function represented by the table below in slope-
intercept form.
X
O
O
1
2
3
4
у
1
3
5
7
9
Please help

Answers

Answer:

y=2x+1, assuming my change in the reported data was correct.

Step-by-step explanation:

The data for x had one more entry than the values for y.  I removed the second "0" so that the x and y points line up, as shown in the attached image.  The data indicate a straight line, with a slope of 2 (y increases by 2 for every x increase of 1).  The y-intercept is 1, as per the first data point (0,1).

How much percentage of a minute is a second?

Answers

1min=60s

Percentage:-

[tex]\\ \sf\longmapsto \dfrac{1}{60}\times 100[/tex]

[tex]\\ \sf\longmapsto \dfrac{10}{6}[/tex]

[tex]\\ \sf\longmapsto 1.6\%[/tex]

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees.


Which best describes why the function is nonlinear?

The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Answers

Answer:

C

Step-by-step explanation:

I think

Answer:

Step-by-step explanation:

d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Number of tree purchased                            Total Cost ($)

               1                                                                 60

               2                                                                120

               3                                                                180

               4                                                                240

               5                                                                290

For the linear function rate of change is constant.

Now, between 2 and 3 trees rate of change is given by

Now, between 3 and 5 trees rate of change is given by

This is clearly that the rate of change isn't constant. Therefore, the function is non-linear.

so,

d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Learn more about linear function here

brainly.com/question/11897796

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Answer fasttt please help!!!

Answers

What the question I will answer fast and fix your help
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