What is a cubic polynomial function in standard form with zeroes 1, –2, and 2?

Answers

Answer 1

Starting off with the polynomial in standard form would be extremely difficult, but we can construct one fairly easily with the zeroes we've been given.

We know from the given zeroes that our function has the value 0 when x = 1, x = -2, and x = 2. Manipulating each equation, we can rewrite them as x - 1 = 0, x + 2 = 0, and x - 2 = 0. To construct our polynomial, we simply use all three of the expressions on the left side of the equation as factors and multiply them together, obtaining:

[tex](x-1)(x+2)(x-2)=0[/tex]

Notice that we can easily obtain each our three zeroes by dividing both sides by the two other factors. From here, we just need to expand the left-hand side of the equation. I'll show the work required here:

[tex](x-1)(x+2)(x-2)=0\\ \big[(x-1)x+(x-1)2\big](x-2)=0\\ (x^2-x+2x-2)(x-2)=0\\ (x^2+x-2)(x-2)=0\\ (x^2+x-2)x-(x^2+x-2)2=0\\ x^3+x^2-2x-(2x^2+2x-4)=0\\ x^3+x^2-2x-2x^2-2x+4=0\\ x^3+(x^2-2x^2)+(-2x-2x)+4=0\\ x^3-x^2-4x+4=0\\[/tex]

So, in standard form, our cubic polynomial would be [tex]x^3-x^2-4x+4[/tex]

Related Questions

The area of a square bedroom is 144 square feet. what is the length of one wall?

Answers

The answer is: "12 feet" .
________________________________
Note: In a square, the length of EACH of the four sides of the square is the same.

Area = Length * width.

For a square, length = width.

So for a square, Area = length * width = (length of a side)² = s² ,

Given: A = s² = 144 ft² ;

Solve for the positive value of "s" .
________________________________
  → s² = 144 ft² ; Take the "square root" of each side ;

  → √(s²) = √(144 ft²) ;

  → s = 12 ft.
_______________________________
The answer is: 12 ft.
_______________________________

The length of one wall of the bedroom is 12 feet, which is the square root of the room's area of 144 square feet

The area of a square is calculated by squaring the length of one of its sides, so if the area of a square bedroom is 144 square feet, the length of one side can be found by taking the square root of the area. Therefore, to find the length of one wall, calculate the square root of 144, which is 12 feet. So, the length of one wall of the bedroom is 12 feet

PLEASE HELP ASAP!! Will give brainliest!

1)100,1000,10,000, or 100,000

2)Greater or less

Answers

Hi there! 9.125 * 10^-3 is definitely less than 9.125 * 10^2, because when it comes to negative powers of 10, the numbers are decimals. 10^-3 equals 0.001 or one thousandths in word form. 10^2 is 100. When solving for the answers. 0.009125 is less than 912.5. When 912.5 is divided by 0.009125 912.5 is 100^5 or 100,000 times greater than 0.009125. The answer is that 9.125 * 10^-3 is 100,000 (100^5) times less than 9.125 * 10^2.

the awnser to this question is less than

A tortoise and a hare are competing in a race around a 1600-meter track. The arrogant hare decides to let the tortoise have a 780-meter head start. When the start gun is fired the hare begins running at a constant speed of 10 meters per second and the tortoise begins crawling at a constant speed of 5.3 meters per second.

Answers

I am presuming that the question is who won or by how much did the winner win.

distance equals rate times time, or d = r*t
For the Hare d = 1600 and r = 10
1600 = 10 t
Divide both sides by 10
t = 160
The hare finished in 160 seconds

For the tortoise d = 1600 - 780 = 820 (due to the head start) and r = 5.3
820= 5.3 t
Divide both sides by 5.3
t = 154.72 (rounded to the hundredths place)

The tortoise won by 5. 28 seconds (160-154.72)

The tortoise wins. The tortoise takes 154.7 seconds to finish the race. The hare takes 160 seconds to finish the race. There really isn't a question here, but I'm going to assume the unasked question is one of "Who wins?" "How long does it take the tortoise to complete the race?" or "How long does it take the hare to complete the race?" And thankfully, in determining the answer to "Who wins?" will have as a side effect the answers to the other two questions. First, how many seconds does it take for the hare to complete the race. Just divide the distance by the speed and you'll have the answer. So 1600 m / 10 m/s = 160 s Now, how many seconds does it take the tortoise to finish the race? Same thing. Distance divided by speed. But there's a twist, you need to figure out the distance. And that is just the track length minus the head start. So (1600 m - 780 m) / 5.3 m/s = 820 m / 5.3 m/s = 154.717 s And since the tortoise took less time than the hare, the tortoise wins.

Two angles are complementary. the measure of one angle is 21 more than the measure of the other angle. find the measures of the angles

Answers

The angles would be 34.5 degrees and 55.5 degrees

Pythagorean Theorem. I need help please!!!!!

Answers

The hikers started at point S.
The first hiker went 2 miles east and 1 mile north to point A.
The second hiker went 1 mile west and 3 miles south to point B.
See the figure below.

                                                              A
                                                        I
                           1 mile                       I    1 mile
                          I---------S------------------I
                          I                2 miles
                          I
                          I
            3 miles   I
                          I
                          I
                          B

Now we need to see how much east and how much north hiker B is from hiker A.

                                                            A
                                                        I
                           1 mile                       I    1 mile
                          I---------S------------------I
                          I                2 miles   I
                          I                                   I
                          I                                   I
            3 miles   I                                   I   3 miles
                          I                                   I
                          I                                   I
                          B----------------------------I
                                         3 miles

From point B go 3 miles east, then 3 + 1 = 4 miles north to point B.
The distance between the hikers is the hypotenuse of a triangle with legs of lengths 3 and 4.

3^2 + 4^2 = d^2

9 + 16 = d^2

d^2 = 25

d = 5

The distance between the hikers is 5 miles.

Carl is boarding a plane. He has 2 checked bags of equal weight and a backpack that weighs 4 kg. The total weight of Carl's baggage is 35 kg. Write an equation to determine the weight, (w), of each of Carl's checked bags.

Answers

(35 - 4) / 2 = w
35 is total weight
4 is backpack
2 is the number of bags

Answer:

15.5

Step-by-step explanation:

2w+ 4 = 35 is the equation

15.5 is the total for w

I did this khan and this answer is correct

Hope this helps!

4. The science team uses the information to suggest the main outcome of the hypothesis.

a. Make a prediction
b. Test the hypothesis
c. observe the problem
d. Define a problem

5. This step includes recording data, taking photos, and coordinating information.

a. Make a prediction
b. Test the hypothesis
c. observe the problem
d. Define a problem

Answers

4- B
5- C

Hoped I helped!

Hi Heres your Answer!
4.A
5.B
Hope this is right!
Let me Know!

What is the output of the function f(x) = x + 21 if the input is 4? When the input is 4, the output of f(x) = x + 21 is

Answers

To find the output when you know the input, just plug the input into the function.

x+21=4+21=25

The output is 25.

Hope this helps!

The answer is

hope that helps

You spend 5/6 of the money in your pocket on new clothes for school. The amount you spend on jeans for school is 2/5 of the total amount you spend on all your school clothes.
What fraction of the original amount of money in your pocket do you spend on jeans?

Answers

If the amount of money you spend in total is 5/6, and you spend 2/5ths of that on jeans, then 2/5 of 5/6 is what you want to get. To get that, we simply multiply the two to get 10/30 or 1/3 by dividing both the numerator and denominator by 10

What is the y-intercept of the line? y +6x - 4y-intercept =?

Answers

Slope intercept form is always y=mx+b where your m is your slope and your b is your y-intercept. Knowing this we first need to put your equation into slope intercept form. to do this all we have to do is subtract everything except why across an equal sign to get y=-6x+4. Now all you have to do is figure out what the 'b' is to know that the y-intercept is 4

Answer:

[tex]\huge\boxed{\boxed{\tt{the \ y-intercept \ is \ -4}}}[/tex]

Step-by-step explanation:

Hello.

The equation is written in slope-intercept form (y-mx+b, where m stands for the slope of the line and b stands for the y-intercept)

Let's write the equation and see if we can identify its y-intercept (the point where the graph touches the y-axis)

Equation:

[tex]{\boxed{\boxed{\bf{y=6x-4}}}[/tex]

Y-intercept:

[tex]\boxed{\boxed{-4}}[/tex]

And we're done!

Note: The slope of the line is 6.

I hope it helps & have an outstanding day!

~ST2710

Interpret the graph to determine the statement the manager at a building supply store can use to help a customer determine how much primer to purchase.
Each gallon of primer will cover a (minimum) (maximum) (multiple) of (200) (400)(600) square feet

Answers

Answer:

Each gallon of primer will cover a maximum of 200 square feet

Step-by-step explanation:

The x-axis of the graph is the area to paint in square feet. The y-axis of the graph is the number of gallons of primer needed.

We can see that 1 gallon of primer covers from 0 to 200 feet; 2 gallons of primer covers from 200 to 400 feet; etc.

This tells us that each gallon of primer covers a maximum of 200 square feet.

A tortoise walk 52.0 feet per hour. Convert this into inches per minute

Answers

1 foot = 12 inches

52 * 12 = 624 inches per hour

1 hour = 60 minutes

624/60 = 10.4 inches per minute

The Scott Shop charges $27 more than the Garcia Co. for a winter jacket. If the Scott shop’s price is $77, how much does the Garcia Co. charge?

Answers

Garcia Co. charge = 77 - 27 = $50

subract 27 from 77

77 -27 =50

Garcia charges 50 dollars

I’m stuck. Please help.

Answers

So, we want to first make this into equation form.

Say n = the number.

4 less:

-4

Than half a number

1/2n - 4

Is equal to 37 less

1/2n - 4 = -37

Than twice the number

1/2n - 4 = 2n - 37

So, move all like terms to the same side:

1/2n - 2n = -37 + 4

-1 1/2n = -34

/-1 1/2 /- 1 1/2

n = 22 2/3

a rectangle has a diagonal which is 4 times the width if the area is 15root2 what are width andperimeter of the rectangle

Answers

Let width be x
Area: 15√2
Diagonal; 4x

First, you need to find the length using pythagorean theorem.
a=x
c=4x
b=?

Solve this in terms of x and you will find the solution to be; √15x²

Knowing this, plug the number back into the area formula to find the value of x,

(x)(√15x²)=15√2
...
..
x⁴=30

Length= √(15√(30))

Do the calculations just to be sure

Hope I helped :)

Soft drinks are sold in 2-liter bottles or 354-milliliter containers. How many liters are in 354 milliliters? please explain well

Answers

The answer is 0.354 liters.

0.354. A liter is 1000 milliliters so just out a 0. Behind the number

To maximize learning, a ________ should be presented on a(n) ________ schedule.

Answers

To maximize learning, a CS + UCS should be presented on a(n) continuous schedule.

In here, CS means conditional stimulus while UCS is the unconditioned stimulus. Taking for example, let us imagine that the smell of food is the unconditioned stimulus, the feeling of hunger in response to that specific smell is a unconditioned response, and then the sound of the whistle is the conditioned stimulus.

How is the graph of y=9(3)^x+6 translated from the graph of y=9(3)^x?

Answers

it is translated down 6.

what two integers does Square Root 140 fall between?

Answers

Answer: "11 and 12" .
_______________________________
11² = 121 ;
12² = 144;

140 falls between 121 and 144 .
_______________________________

Answer: "11 and 12"
hope this helps:D

Suppose the number $1155$ is written as the product of three positive integers. What is the smallest possible value of the sum of those three integers?

Answers

First off, let us find for the prime factors of this number, 1155. The prime factors are:

3 * 5 * 7 * 11 = 1155

3, 5, 7, 11

Since there are 4 prime factors, we multiply the two smallest prime factors to make this into three, so multiply 3 and 5, so:

15, 7, 11

Now the smallest possible sum is:

15 + 7 + 11 = 33

Answer:

How many seconds are there in (a) one hour and thirty-five minutes and (b) one day?

Answers

There are 5700 seconds in an hour.

what is the least common factor of 54 and 77

Answers

sorryyyyyyyyyyyyyyyyyyyyyyyyyyyy go see in goggle

I need help from a math genius

Answers

The answer to the first one is (B. 24)

The answer to the second is (B. 14)

1. 24=38+(8/8)
2. 14=6+8
3. 5=2+3
4. 10=2X5

The floor of a shed has an area of 99 square feet. the floor is in the shape of a rectangle whose length is 7 feet less than twice the width. find the length and the width of the floor of the shed. use the formula, area equals=length times•width.

Answers

W=width, L=length
L=2W-7
LxW=99 (now substitute)
(2W-7)xW=99 (distribute W)
2W²-7W=99
2W²-7W-99=0 (set to 0 to solve)
(W-18/2)(W+9/2)=0
(W-9)(2W+9)=0
W-9=0; W=9
2W+9=0; 2w=(-9) not possible in real world to have a negative length
So, width = 9 ft, and length = 2(9)-7 = 11 ft

Final answer:

The width is 9 feet and the length is 11 feet.

Explanation:

The area of a shed floor is given as 99 square feet, and the floor is shaped like a rectangle. According to the problem, the length (L) of the floor is 7 feet less than twice the width (W). The relationship between length and width can be expressed as L = 2W - 7. We can use the area formula, which is Area = Length × Width.

Given the area (A) is 99 sq ft, we can set up the equation:

A = L × W
99 = (2W - 7) × W

Now we solve for W using the quadratic equation:

W2 - 7W + 99 = 0

Upon solving, we find that W = 9 feet (since the width cannot be negative). Now we can find the length L by substituting W into the length expression:

L = 2 × 9 - 7 = 11 feet

Therefore, the width is 9 feet and the length is 11 feet.

Ashley is making cookies. the recipe calls for 3/4 of a cup of sugar. she needs to make five batches of cookies. how many cups of sugar does ashley need?

Answers

Ashley needs 3 3/4 cups of sugar.
Hope this helps!!

If t varies directly as s and inversely as v^2 and is t =0.1 when s =72 and v=6, find s when t=5 and v=0.2

Answers

Attached the solution and work.

Write an expression that is equivalent to 2/3 (4x + 9).

8/3x + 6

8/3x + 9

2/3x + 6

2/3x + 9

Answers

2/3 (4x + 9)
= 8/3x + 6

answer
8/3x + 6

2/3 of 9 = 6

2/3 *4 = 8/3

so the answer would be 8/3x +6

At 12:00 noon two mississippi steamboats are 126 miles apart. at 6:00 p.m. they pass each other going in opposite directions. if one steamboat travels 9 miles per hour faster than the other, find the speed of both boats.

Answers

Let us solve the problem using an equation. Let x be the speed of one of the boats. The speed of the other boat will be x + 9. Both the boats have traveled for 6 hours, starting from 12:00 noon to 6:pm The distance they have traveled within 6 hours is 126 miles. The distance traveled by the first boat is x*6 = 6x Miles The distance traveled by the other boat is (x + 9) 6 = 6x + 54 Miles Thus, 6x + 6x + 54 = 126 Miles 12x = 126 - 54 12x = 72 x = 72/12 x = 6 So the speed of one of the boats is 6 miles per hour and the speed of the other boats is 6 + 9 = 15 miles per hour.

The answer will be

The rate of the first steamboat is 6 mph, the rate of the second steamboat is

15 mph .

Amanda walks at an average speed of 3.5 miles per hour. The function d(x) gives the distance Amanda walks in x hours

Answers

d = 3.5

If she walks 3.5 miles per hour. The amount would multiply x. So you just have 3.5(x).

The perimeter of the triangle shown to the right is 115 feet . Find the length of each side

Answers

Final answer:

To find the length of each side of the triangle, we need to determine the length of the third side. The perimeter of the triangle is given as 115 feet. We know that the first side is 80 feet long and the second side is 105 feet long. To find the length of the third side, we subtract the sum of the lengths of the first two sides from the perimeter: 115 - 80 - 105 = 115 - 185 = -70.

Explanation:

However, since the length of a side cannot be negative, it means that there has been an error in the measurements or calculations. Please double-check the given information and calculations to ensure the accuracy of the question.

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