What is the completely factored form of f(x) = x3 – 2x2 – 5x 6? f(x) = (x 2)(x – 3)(x 6) f(x) = (x 2)(x – 3)(x – 6) f(x) = (x – 2)(x 3)(x – 1) f(x) = (x 2)(x – 3)(x – 1)

Answers

Answer 1

[tex]x^3-2x^2-5x +6\\\\=x^3-x^2-x^2+x-6x+6\\\\=x^2(x-1)-x(x-1)-6(x-1)\\\\=(x-1)(x^2 -x -6)\\\\=(x-1)(x^2 -3x +2x -6)\\\\=(x-1)\textbf{[} x(x-3) +2(x-3)\textbf{]}\\\\=(x-1)(x-3)(x+2)[/tex]

Answer 2

The requried, factored form of the given expression is (x - 1)(x - 3)(x + 2).

What are the factors?

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

To factor the polynomial f(x) = x³ – 2x² – 5x + 6 completely, we can use a combination of the rational root theorem and synthetic division.

We can use synthetic division to test each possible root and see if it is a factor of the polynomial. Starting with x = 2, we have:

2 | 1 -2 -5 6

  | 2 0 -10

  |_____________

1 0 -5 -4

Since the remainder is not zero, x = 2 is not a factor of the polynomial. Continuing with the other possible roots, we find that x = 1 and x = 3 are roots, but x = -1, x = -2, x = -3, and x = -6 are not roots.

Therefore, we can factor the polynomial as follows:

f(x) = x² – 2x² – 5x + 6

= (x - 1)(x - 3)(x + 2)

So the completely factored form of f(x) is f(x) = (x - 1)(x - 3)(x + 2).

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Related Questions

What will be the coordinates of point A after a reflection across the x-axis?



A
(6,−2)

B
(6,−5)

C
(−1,5)

D
(−6,5)

Answers

Answer:

OPTION B

Step-by-step explanation:

(6,-5)

I HOPE IT HELPED YOU

PLEASE HURRY!!!!!
EXPLAIN why or why not.

Answers

Answer:

The graph is not a line of best fit as there are not an equal number of data points on each side of the line

Step-by-step explanation:

Brainliest would be appreciated

please answer this question ​

Answers

Answer:

e

Step-by-step explanation:

the coordinates of the midpoint are the average of the coordinates of the endpoints.

let coordinates of C = (x, y ) , then with A = (- 1, 2 ) calculate the average and equate to the coordinates of B (3, 2 )

[tex]\frac{x-1}{2}[/tex] = 3 ( multiply both sides by 2 to clear the fraction )

x - 1 = 6 ( add 1 to both sides )

x = 7

and

[tex]\frac{y+2}{2}[/tex] = 2 ( multiply both sides by 2 )

y + 2 = 4 ( subtract 2 from both sides )

y = 2

coordinates of C = (7, 2 )

What is the length of leg s of the triangle below?

Answers

Answer:

[tex]\bf F.\;8[/tex]

Step-by-step explanation:

[tex]\bf Sin (45^o)=\cfrac{5}{8\sqrt{2} }[/tex]

[tex]\bf \cfrac{1}{\sqrt{2} } =\cfrac{S}{8\sqrt{2} }[/tex]

[tex]\bf S=\cfrac{8\sqrt{2} }{\sqrt{2} }[/tex]

Cancel common factor:- √(2)

[tex]\bf S=8[/tex]

Therefore, your answer is f) 8.

what is the solution to the exponential equation (½)x = 32

Answers

Answer:

Step-by-step explanation:

log(1/2) (32) =x

Ik this isn’t a math question but I want to know how much this beanie boo is cause I’m planning on selling it

Answers

Step-by-step explanation:

That's a rare Halo II angel bear, especially since it has a brown nose. Don't sell it less than $40, you can check prices on many websites

Nice why are u selling it?

simplify 2 + 5(1 + 8n)

Answers

Answer:

7+40n

Step-by-step explanation:

distribute 5 and get 5=40n then add the extra 2 for the awnser of 7=40n

Answer:

7+40n

Step-by-step explanation:

expand 5(1+8n)= 5+40n=

2+5+40n

= 7+40n

need some help with the question in the image

Cheers ​

Answers

a) 5000 m
b) 0.65 cm
c) 1.78 m
d) 3kg

Find the volume of the following rectangular prism in terms of x, if the length is 4x + 0. 5, the width is 1/2 x, and the depth is x -2

Answers

The  volume of the following rectangular prism in terms of x is 4x+ 0.5)(0.5x)(x - 2)

Volume of a prism

The formula for calculating the volume of a prism is expressed as

V = lwh

l is the length

w is the width

h is the height

Given the following

l =4x + 0.5

w = 1/2x

h = x - 2

Find the volume

V(x) = (4x+ 0.5)(0.5x)(x - 2)

Hence the  volume of the following rectangular prism in terms of x is 4x+ 0.5)(0.5x)(x - 2)

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What does this data mean in terms of likelihood for a person from a particular geographic area to be dairy tolerant

Answers

The data shows a person from regions such as Northern Europe, Middle East 2, and East Africa will have a high dairy tolerance.

What is Dairy tolerance?

This is characterized by unpleasant symptoms when the body doesn't produce enough lactase to digest the lactose consumed.

From the data, the regions which shows high dairy tolerance are those from Northern Europe, Middle East 2, and East Africa.

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Mrs. Johnson bought 12 pound of ham and used it to make 3 sandwiches. She uses the same amount of ham on each sandwich. What fraction of a pound of ham is on each sandwich

Answers

The fraction of a pound of ham that each sandwich has for the case when Mrs Johson used 12 pounds of ham to make 3 sandwiches is 4 pound per ham. or 4/1

How to interpret the division?

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus, [tex]a \div b =[/tex] a divided in b equal parts.

Also, we can write: [tex]a \div b = a \times \dfrac{1}{b}[/tex]

(it is since a = a times 1 so [tex]a/b = 1 \times (a/b) = (1/b) \times a[/tex])

For this case, we're specified that:

Total ham Mrs. Johnson bought = 12 poundsTotal sandwiches that she makes of that amount of ham = 3

12 pound of ham is divided in 3 parts for 3 sandwiches (assuming equally divided).

That means:

Amount of ham each sandwich gets = 12 divided by 3 = 12/3 = 4 pounds.

To find the fraction of a pound of ham that is on each sandwich, we find what part of a pound is 4 pounds.

If we take 4 times a pound, then we get 4 pounds.

Thus, 4 of a pound = 4 pound

In fraction, we have: 4 pounds = 4/1 fraction of a pound.

Thus, the fraction of a pound of ham that each sandwich has for the case when Mrs Johson used 12 pounds of ham to make 3 sandwiches is 4 pound per ham. or 4/1 fraction of a pound

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PLS HELP FAST!!
What is the mean of this data set?

3, 5, 10, 11, 15

Answers

Answer:

8.8

Step-by-step explanation:

To find mean, add all of the numbers together, then divide that sum by how many numbers there are.

3 + 5 + 10 + 11 + 15 = 44

44 ÷ 5 = 8.8

hope this helps!

Step-by-step explanation:

3+5+10+11+15÷5=

44 divided by 5 which gives 8.4

therefore that is the mean hope this helps

PLEASE HELP MEEEE!!!!! 20 POINTS + BRAINLYEST!!!
(No links please)

If a right triangle has a hypotenuse of 13 inches and a leg of 5 inches, how could you use the Pythagorean Theorem to find the missing side? What is the length of the missing side?

A tree casts a 13-foot shadow. The distance from the top of the tree to the far end of the shadow is 22 feet. If the tree is perfectly straight and creates a right angle with the ground. How tall is the tree?

How can you use the Pythagorean Theorem to find the distance between two points on the coordinate plane?
A cone has a radius of 6 inches and a height of 11 inches. What is the volume of the cone?

Answers

Answer:

1)  46.64

2)  17.75

3)  414.69

Step-by-step explanation:

13^2 -5^2=sqrt2172=46.64

22^2-13^2=sqrt315=17.75

V=πr2h

11/3=π·62·11

11/3≈414.69

SOLVE CORRECTLY FOR BRAINLIEST! QUESTION DISPLAYED BELOW:

Answers

Answer:

2

Step-by-step explanation:

We are given:

t = -11
u = 11
v = 1

Plug in the values to (tv-u) / tv:

((-11)(1) - 11) / (-11)1
(-11-11) / -11
-22 / -11
= 2

URGENTLY NEEDING HELP!!!!

Answers

Answer:

(6,-1)

Step-by-step explanation:

it's given 2m and m is at point (4,-3) increasing each point by 2 = (6,-1).

not sure

On average, what value is expected for the f-ratio if the null hypothesis is true?.

Answers

The expected value of the f-ratio is the mean value

On average, the expected value for the f-ratio is 1.00 if the null hypothesis is true

How to determine the expected value?

From the question, we understand that the null hypothesis is true and the distribution is the F-ratio

The above scenario means that:

The variance of the top and the bottom ratio are the same

When the ratios are the same and the null hypothesis is accepted, then the expected value is 1.00

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Zachary's cornfields are irrigated in circular regions. Zachary records data on the corn production from various irrigated circular regions,

Radius (ft)

500

1,000

1,500

2,000

2. 500

Bushels of Corn

2,705

10,818

24 341

43,273

67,613

What type of function best models the given data set?

A constant

B. Exponential

C. Linear

D. Quadratic

Answers

Answer:

Quadratic

Step-by-step explanation:

2705/500 = 5.41
10,818/1000 = 10.818
24 341/1,500 =24.227

43,273/2000 = 21.6365
67,613/2500 = 27.0452

Rate of change changes

Jenna bought 3 shirts for $62.25 if each shirt cost the same amount what is the cost of one shirt

Answers

Answer:

The cost of one shirt is $20.75.

Step-by-step explanation:

Total Cost/3 Shirts = The Cost of 1 Shirt

62.25/3 = 20.75

How many 15° angles are in a circle?
Enter your answer in the box.
angles

Answers

Answer:

24

Step-by-step explanation:

a circle is 360

we can divide 360 by 15

360 divided by 15 =

24

If x is a positive acute angle and cos x = 1/2, what is the value of sin 1/2 x?

A)1
B)2
C) square root 3/ 2
D)1/2

Answers

It is B cause I just know I’m right

Find the surface area of the prism.

HEEEELP PLEASE!!!!!

Answers

Part I: Renaming the faces of the prism

Let the vertices of the prism be A, B, C, D, E, F, G, and H. (Refer to image).

From the image, we can tell that the faces of the prism are:

ABFG    HDCE     FBCE     GADH     GFEH    ABCD

Part II: Recalling the surface area formula

Surface area formula:

[tex]\text{Surface area = Sum of the area of it's faces}[/tex]

The faces are ABFG, HDCE, FBCE, GADH, GFEH, and ABCD (Previous Part)

[tex]\implies \text{SA = A(ABFG) + A(HDCE) + A(FBCE) + A(GADH) + A(GFEH) + A(ABCD)}[/tex]

Part III: Determining the surface area of the prism

If we look at the prism carefully, we can tell that:

ABFG = DCEH

GADH = FBCE

GFEH = ABCD

Therefore, the new equation is:

[tex]\implies \text{SA = 2[A(ABFG)] + 2[A(GADH)] + 2[A(GFEH)]}[/tex]

If we look carefully, we can see that GADH and ABFG are rectangles. Therefore, their areas will be length multiplied by width. Now, substitute the dimensions of the rectangles in the surface area.

[tex]\implies \text{SA} = 2[4 \times 4] + 2[2.5 \times 4] + \text{2[A(GFEH)]}[/tex]

The area of a parallelogram is the base multiplied by the height.

[tex]\implies \text{SA}= 2[4 \times 4] + 2[2.5 \times4] + 2[4 \times 2]}[/tex]

Finally, simplify the equation to determine the surface area.

[tex]\implies \text{SA} = 2[16] + 2[10] + 2[8][/tex]

[tex]\implies \text{SA} = 32 + 20 + 16[/tex]

[tex]\implies \boxed{\text{SA = 68 m}^{2} }[/tex]

A triangle has a perimeter of 16x + 4. If Side 1 is 3x + 2, Side 2 is 8x + 7, what is the measure of Side 3? Show your work

Answers

Answer:

Side 3 = a - 2

Step-by-step explanation:

Perimeter of a ∆ = sum of all the sides of a triangle

Perimeter of the given ∆ = 6a + 3 units

Side 1 = 2(a + 3)

Side 2 = 3a - 1

Side 3 = ?

Therefore:

Side 3 = Perimeter - sum of side 1 and 2

Thus:

Side 3 = 6a + 3 - [2(a + 3) + (3a - 1)]

Side 3 = 6a + 3 - [2a + 6 + 3a - 1]

Side 3 = 6a + 3 - [5a + 5]

Side 3 = 6a + 3 - 5a - 5

Side 3 = a - 2

Step-by-step explanation:

Describe the pattern in the sequence. Find the next two terms of the difference.
-2, -5, -8, -11, ...

Answers

Answer:

-14,-17

I hope this is useful

Number 19. Please!hurry!

Answers

Answer:

Step-by-step explanation:

PLS HELP !!! I just dont understand im not smart-

Answers

Answer:

Let's first find the area of the rectangle/rectangle,

we can do this by combining their lengths as a whole

or

we can individually find their area.

Let's find the area of the individual shapes, upper rectangle;

(using the formula)

A = l x w

Where 'l' represents the length and 'w' stands for the width.

Plug in what you know:-

A = 27(24)

A = 648 square feet is the area of the upper rectangle.

Now, the lower rectangle:

A = l x w

Plug in what you know:-

A = 27(32)

A = 864 square feet is the area of the lower rectangle.

Now we find the area of the triangle beside;

(using the formula)

A = BH x 1/2

Where 'B' represents the base, 'H' the height, and 1/2 means to simply divide the product of those two lengths(base x height) by 2.

Plug in what you know:

A = BH x 1/2

A = 18(32) x 1/2

A = 576 x 1/2

A = 576/2

A = 288 square feet is the area of the triangle beside.

Add up all the areas we've gathered so far:

648 + 864 + 288

= 1,800 square feet is the area of the patio

Answer:

Let's first find the area of the rectangle/rectangle,we can do this by combining their lengths as a wholeorwe can individually find their area.Let's find the area of the individual shapes, upper rectangle;(using the formula)A = l x wWhere 'l' represents the length and 'w' stands for the width.Plug in what you know:-A = 27(24)A = 648 square feet is the area of the upper rectangle.Now, the lower rectangle:A = l x wPlug in what you know:-A = 27(32)A = 864 square feet is the area of the lower rectangle.Now we find the area of the triangle beside;(using the formula)A = BH x 1/2Where 'B' represents the base, 'H' the height, and 1/2 means to simply divide the product of those two lengths(base x height) by 2.Plug in what you know:A = BH x 1/2A = 18(32) x 1/2A = 576 x 1/2A = 576/2A = 288 square feet is the area of the triangle beside.Add up all the areas we've gathered so far:648 + 864 + 288= 1,800 square feet is the area of the patio

Step-by-step explanation:

Mark wants to run his town's half marathon, which covers 13.1 miles. When runners have completed 65% of the course, they are challenged with a steep hill to climb. What distance, in miles, will Mark run before he gets to the foot of the hill? Round your response to the hundredths place.

Answers

Using proportions, it is found that Mark will run 8.52 miles before he gets to the foot of the hill.

What is a proportion?

A proportion is a fraction of a total amount.

In this problem, the distance to the foot of the hill is 65% of 13.1 miles, hence:

d = 0.65 x 13.1 = 8.52 miles.

Mark will run 8.52 miles before he gets to the foot of the hill.

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A cylindrical tank whose diameter and height are 2.1m and 4m respectively is filled with water whose density is 1g/cm^3.calculate the mass of the water in kg.​

Answers

Step-by-step explanation:

I assume it means the task is filled completely.

diameter = 2.1 m

therefore, radius = diameter/2 = 2.1/2 = 1.05 m

height = 4 m

volume of a cylinder is

ground area × height, so

pi×r² × height = pi×1.05²×4 = 13.8544236... m³

1 cm³ is 1g

for 1 kg (remember, "k" stands for "kilo" and means 1000) we need therefore 1000 cm³ (which is a cube of 10 cm side length).

how many cm³ are in 13.8544236... m³ ?

1 m = 100 cm

1 m² = 1 m × 1 m = 100×100 = 10,000 cm²

1 m³ = 1 m × 1 m × 1 m = 100×100×100 = 1,000,000 cm³

that means a factor of 1,000,000 !

so, the volume of the cylinder is

13.8544236... × 1,000,000 = 13,854,423.6... cm³

to get the mass of kg of that much water we need now to divide by 1000 :

13,854,423.6... / 1000 = 13,854.4236... kg

which is, by the way, 13.8544236... tons.

yes, 1 m³ of water is 1 ton ...

I don't know, if you need to round the result.

if you e.g. only need full kg, then the answer would be

13,854 kg.

Which of the following is a possible equation of a parabola. Explain why.

Answers

Answer:

the answer is C

because for an equation to be an equation of a parabola, the coefficient of x^2 and y^2 has to be 1

Trent bought four pounds of deli turkey for $2.68 per pound. How much did he spend? $8.42​

Answers

$10.72
Because Trent bought four pounds, you would multiply $2.68 times 4.

George works at Whataburger. He makes $8. 50 per hour and works a maximum of 25

hours per week. The equation e = 8. 50h can be used to determine the amount of money,

e, that George earns after h hours worked. What is the domain and range that represents

this situation?

A Domain: 0 Shs 25

Range: 0 ses 212. 50

B Domain: Oshs 212. 50

Range: 0 ses 25

C Domain: 8. 50 Range: 0 ses 212. 50

D Domain: Oshs 8. 50

Range: 0 ses 212. 50

Answers

Answer:

200 should be

Step-by-step explanation: mhm yes yes

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