Is (x + 5) a factor of f(x) = x3 − 4x2 + 3x + 7? Use either the remainder theorem or the factor theorem to explain your reasoning. This is worth 100 points. Will mark brainliest. Whatever you want. Please answer this.

Answers

Answer 1

Answer:

(x + 5) is not a factor of, [tex] f(x) = x^ 3 − 4x^2 + 3x + 7 [/tex]

Step-by-step explanation:

[tex] f(x) = x^ 3 − 4x^2 + 3x + 7 \\ \\ let \: x + 5 = 0 \\ \implies \: x = - 5 \\ \\ plug \: x = - 5 \: in \: f(x) \\ \\ f( - 5) = ( - 5)^ 3 − 4( - 5)^2 + 3( - 5) + 7 \\ \\ f( - 5) = - 125 − 4(25) - 3( 5) + 7 \\ \\ f( - 5) = - 125 − 100 - 15 + 7 \\ \\ f( - 5) =7 - 240 \\ \\ f( - 5) = - 233 \\ \\ \because \: f( - 5) \neq 0 \\ \implies \: remainder\: is\: not\: zero\\ \therefore \: (x + 5) \: is \: not \: a \: factor \: of \: \\ f(x) = x^ 3 − 4x^2 + 3x + 7 \\ [/tex]

Answer 2
I’m gonna use the remainder theorem so if a polynomial p(x) is divided by x-a the remainder obtained is p(a) therefore

X= -5

Then just plug in -5 in the function and if the result is 0 then is a factor

(-5)^3 - 4(-5)^2 + 3(-5) + 7 = -233

Therefore x+5 is not a factor

Related Questions

Mackenzie built the small lego set it cost $5.49 Caleb built the large lego set how much do you think the large lego set cost

Answers

Answer:

Since there is no available data for the Lego set, it is safe to assume that the cost would be definitely higher than the small Lego set built by Mackenzie. For example, if the dimension of the small Lego set is 50 X 30 X 6 (length X breadth X height all in cm ) which cost Mackenzie $5.49.

On the other-hand, let assume that, the large Lego set built by Caleb is twice that of Mackenzie Lego set (that is 100 X 60 X 12 ), it could be found that, the cost for the large Lego set would cost minimum of $10.98

Step-by-step explanation:

please help me answer this ASAP if u view it then u'll see the question properly
[tex] \frac{1 + \sqrt{3} }{ \sqrt{12} } [/tex]
i will give brainliest answer if it the correct answers ​

Answers

Answer:

1/6 sqrt(3) + 1/2

Step-by-step explanation:

(1 + sqrt(3))

------------------

sqrt(12)

Multiply the top and bottom by sqrt(12)

(1 + sqrt(3)) * sqrt(12)

------------------

sqrt(12)*sqrt(12)

sqrt(12) + sqrt(3) * sqrt(12)

------------------

12

Simplify

sqrt(4)sqrt(3) + 6

------------------------

12

2 sqrt(3) +6

--------------------

12

1/6 sqrt(3) + 1/2

Choose the number that is 5 more than a square number.
21
34
35
65
76

Answers

5 more than a square number would be 21 which is 5 more than 16 (the square of 4)

Answer:

21

Step-by-step explanation:

this requires practical assumption.

take 9 for example

5 more than 9 means 9 - 5 = 4

4 is a square number

21 = 21 - 5 = 16

16 is a square number

34 = 34 - 5 = 29

29 is not a square number

35 = 35 - 5 = 30

30 is not a square number

65 = 65 - 5 = 60

60 is not a square number

76 = 76 - 5 = 71

71 is not a square number

Question 6: please help me out here :(((

Answers

Answer:

m∠1 = 106

Step-by-step explanation:

Given: m∠5 = 106

Vertical angles are congruent

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent.

Therefore: m∠1 = 106

32. Exercise Ahmit gets
exercise on the weekend by
working around the house.
On Saturday, he worked for
3 hours mowing the lawn and
raking leaves; He burned
885 Calories.
a. Write a system of
equations that can be used
to describe the amount
of time Ahmit worked and
the number of Calories
he burned by mowing
and raking
b. Determine how much time Ahmit spent on mowing and raking.

Answers

Answer:

X: time mowing lawn (325 Cal/hour)

Y:time raking leaves (275 Cal/hour)

325X + 275Y = 885

3 - X = Y

(1.2 hours mowing the lawn, 1.8 hours raking leaves)

Step-by-step explanation:

you forgot to include vital information. When ahmit rakes leaves, he loses 275 calories per hour. When he mows the lawn, he loses 325 calories per hour according to the textbook you got this from. If he works for 3 hours, you need to find the portion of each activity he did by working backwards from the total calories lost, 885.

A truck moves 3 km in 30 min and and returns at same distance in 20 min find average speed

Answers

Answer:

Step-by-step explanation:

the truck mover 3 km one way, 3 km back, so he moves 6 km

one way the truck needs 30 min, on the way back 20 min

so we have 6 km in 50 min

v=distance/time

v one way=3km/30 min=0.1 km/min

v on the way back=3 km/20min=0.15 km/min

v average =0.1+0.15=0.125 km/min

or 7.5 km/hour

A small submarine travels at a speed of 2.4 km per hour. How far will the submarine travel in 0.25 hours

Answers

Answer:

a

TRUST ME

Step-by-step explanation:

PLEASE MAKE ME BRANLIEST

Answer:

[tex]\boxed {\boxed {\sf A. \ 0.60 \ km}}[/tex]

Step-by-step explanation:

Distance (how far the submarine travelled) can be found by multiplying the speed by the time.

[tex]d=s*t[/tex]

The speed is 2.4 kilometers per hour.

The time is 0.25 hours.

[tex]s= 2.4 \ km/hr \\t= 0.25 \ hr[/tex]

Substitute the values into the formula.

[tex]d= 2.4 \ km/hr * 0.25 \ hr[/tex]

Multiply. Note that the hours (hr) will cancel each other out.

[tex]d= 0.6 \ km/hr *hr[/tex]

[tex]d= 0.6 \ km[/tex]

The submarine travelled 0.6 kilometers in 0.25 hours.

Consider the expression 103 x 0.006. a) What is the exponent in the power of 10? [ Select ] b) How many factors of 10 are in 103? [ Select ] c) How do your answers to the last two questions relate to one another? [ Select ] d) What is the value of 103 x 0.006? [ Select ]

Answers

Solution :

Given that the expression is :

[tex]$10^3 \times 0.006$[/tex]

This can be written as,

[tex]$\Rightarrow 10^3 \times \frac{6}{1000}$[/tex]

[tex]$\Rightarrow 10^3 \times \frac{6}{10^3}$[/tex]

[tex]$\Rightarrow 10^0 \times 6$[/tex]

a). Therefore the exponent in the power of 10

     = 0

b). Factors of 10 in [tex]$10^3$[/tex]

    = 10 x 10 x 10

    = 1000

    = [tex]$10^3$[/tex]

   So there are 3 factors of 10 in [tex]$10^3$[/tex]

c). If we compare the exponent of power of 10 in 1000 and factors of 10 in 1000, then both of them will be same.

  But in part a), we are finding exponent in the power of 10 in the expression  which is equal to 0. And in part b), we are finding the factor of 10 in 1000, which is equal to 3, as 10 x 10 x 10 = 1000.

d). The value of the expression [tex]$10^3 \times 0.006$[/tex] is 6.

If 7 pounds cost $5.46, find the cost of 3 pounds. ​

Answers

Answer:

$2.19

Step-by-step explanation:

7 divided by 3 is 2.5

5.46 divided by 2.5 is 2.184

round it and get 2.19

whats the geometric mean of 1/2 and 8

Answers

Answer:

4

Step-by-step explanation:

1/2 of 8 is 4

Answer is 2. Geometric mean takes the n-th root of the product of the values. So 1/2*8=4, and since there are two numbers, you take the 1/2 root or square root.

So the answer is the square root of 4 which is 2.

solve for x
3(x - 2) = 6x - 12

Answers

Answer:

The answer is 2

Step-by-step explanation:

Here's how I got it:

3(x - 2) = 6x - 12

Multiply 3 times x and 3 times 2, this is what you would get

3x - 6 = 6x - 12

Then, subtract the lowest x with the bigger X, this way you would have x on one side:

3x - 6 = 6x - 12

-3x        -3x

This is what you should have after this:

-6 = 3x - 12

Now, to get the variable (letter that represents a number) by itself, you have to add 12 to both sides like this:

-6 = 3x - 12

+12        +12

You would get this:

6 = 3x

Finally, you have to get x by itself, so you have to divide 3 on both sides like this

6/3 = 3/3 x

That's why, your answer is 2

geometry help please :)

Answers

Answer:

Medium to Line AC

Altitude to Line AC

Bisector of Angle B

Perpendicular bisector of Line AC

Step-by-step explanation:

We can tell that the Medium here is from line AC to angle B. The line is connecting the angle to the middle of the line, making it the medium and altitude. It is also a bisector of angle B because it is directly in the middle of that angle. It is a perpendicular bisector to line AC because it forms a 90 degree angle on the bottom.

#teamtrees #WAP (Water And Plant)

Find the length of AB
AB=
ft (Round to two decimal places)
c
P
A
8 ft
45°
B

Answers

AB= 45 degrees central angle theorem

Kayla can write 415 pages in 10 minutes. At this rate, how many pages could Kayla write in 30 minutes?

Answers

Answer:

1245

Step-by-step explanation:

You have to multiply 415 and 3, since 10 x 3 = 30

415 x 3 = 1245

Answer:

She can write 1245 pages in 30 mins.

Step-by-step explanation:

If 10*3= 30 then multiply 415 by 3 or add 415 3 times and you will get your answer. Hope this helped you!! Give brainliest.

Savannah and Reagan both work in a grocery store. They each stocked the same number of shelves last Saturday, but it took Reagan less time. They've been told that they'll spend their entire 4-hour shifts next Saturday stocking shelves. If their average speeds are consistent, who will likely stock more shelves next Saturday?

HELP!

Answers

Answer:

Reagan

Explanation:

Since Reagan is able to stock the same number of shelves as Savannah while spending less time to do so, it means that Reagan is able to stock shelves faster than Savannah, thus Reagan is able to stock more shelves than Savannah given that their average speeds are constant and that they both work under 4-hour shifts.

Hope this helps :)

Which range contains the value of sqrt(25-4+16)?
A. Between 6.0and 6.2
B. Between 6.9 and 7.1
C. Between 2.1 and 2.3
D. Between 18.4 and 18.6

Answers

Answer:

I wanna say C. But I'm not exactly sure.

Step-by-step explanation:

I hope it's right :(

I Need Help ASAP!!!​

Answers

Answer:f(x) in order from left to right= -20, 5, 10, 15, 30 i.) -.06 ii.)-40

Step-by-step explanation: f(x) is the answer of 5 times whatever x is, so when it’s telling you what x is all you have to is multiply it by the number next to x which in this case is 5. after doing that you get the answers above. for i.) it’s telling you the answer which is -3, so you divide that by 5 getting -.06. In ii.) it gives you x which is -8 so you plug that in giving you -40.

Pleaseee I need help

Answers

Answer:

(48-8xy)-(3xy-10)

Step-by-step explanation:

the green shape is a dilation of the black shape.what is the scale factor of the dilation? ​

Answers

Answer:  5

Step-by-step explanation:

Scale factor = [tex]\dfrac{\text{ side length of image}}{\text{Side-length of original figure}}[/tex]

Given: Black triangle ( original) having perpendicular with length 4 units.  [2 blocks above and 2 boxes below the x-axis ]

Green triangle ( image) having corresponding side as 20 units  [10 blocks above and 10 boxes below the x-axis ].

Scale factor of dilation = [tex]\dfrac{20}{4}=5[/tex]

Hence, the scale factor of the dilation = 5

Of the four choices given, which two, when written as a system, have a solution of (-4,5)?

Answers

Answer:

The answer is A. The first one.

I hope this helps. ;)

Answer:

It is A on edge 2020

Step-by-step explanation:

Please help me on this

Answers

Answer:

PAGE 1

8.) d

9.) b

PAGE 2

6.) b

7.) d

PAGE 3

4.) c

5.) a

PAGE 4

1.) c

2.) c

3.) a

PAGE 5

10.) b

11.) d

Step-by-step explanation:

PAGE 1

8.) x - 20 + x + 10 = 180 (collect like terms)

2x - 10 = 180 (add 10 on both sides)

2x = 190 (divide by 2 on both sides)

x = 95

9.) 2y + y = 180 (collect like terms)

3y = 180 (divide by 3 on both sides)

y = 60

x = y ----> x = 60

PAGE 2

6.)  16x - 6 = 90 (add 6 on both sides)

16x = 96 (divide by 16 on both sides)

x = 6

7.) 5x + 30 = 7x (subtract 5x on both sides)

30 = 2x (divide by 2 on both sides)

15 = x

PAGE 3

4.) <8 and <16 are corresponding angles

5.) 180 - 130 = 50

PAGE 4

1.)  HD and GE are skew lines

2.) AC, EG, and BD are parallel to FH

3.) EF, GH, and BF are perpendicular to FH

PAGE 5

10.) | and || only are the only ones correct

11.) l || m, by the Converse of the Consecutive Interior Angles Theorem.

b/c the two angles equal 180 together and one angle is on line l and the other is on line m. This shows they're parallel.

Hope this helps ya!!

Please help! I think of a number, I double it, and then add 3. The result is 19. Write this in the form of an equation and then solve the equation to find the number I was thinking of.

Answers

Answer:

8

Step-by-step explanation:

Y×2+3=19

19-3=16

16÷2=8

You subtract the 3 first to get what the number was when doubled. After getting that number you would divide it by 2 to get the number that you thought of.

help pls, (20 points and brainlist)

Answers

You mean 8 lol and 35

Zoey has a bag that contains orange chews, apple chews, and watermelon chews. She
performs an experiment. Zoey randomly removes a chew from the bag, records the
result, and returns the chew to the bag. Zoey performs the experiment 57 times. The
results are shown below:
A orange chew was selected 39 times.
A apple chew was selected 6 times.
A watermelon chew was selected 12 times.
Based on these results, express the probability that the next chew Zoey removes from
the bag will be apple chew as a decimal to the nearest hundredth.

Answers

Answer: 54%

Step-by-step explanation:

Gina tracks the low temperatures for a city over six days. Identify the days colder than -1.75°F.

Answers

Answer:

Its Monday and Tuesday

Step-by-step explanation:

Answer:

Monday and Tuesday

Step-by-step explanation:

"Days colder than -1.75 F."

Note that in negative numbers the greater negative number contains a lesser value:

Tuesday: -1.9 F < -1.75 F

Monday: -2.5 F < -1.75 F

There are 82 chairs at a birthday party. The chairs need to be lined up in equal-sized rows. How many possible ways can the chairs be lined up

Answers

Answer:

2 rows of 41

Step-by-step explanation:

i had the same question

The number of possible ways can the chairs be lined up is 2 rows of 41.

Given that,

There are 82 chairs at a birthday party. The chairs need to be lined up in equal-sized rows.

Based on the above information, the calculation is as follows:

[tex]= 2 \times 41[/tex]

= 82 chairs

Here 2 denotes the rows.

Therefore we can conclude that the number of possible ways can the chairs be lined up is 2 rows of 41.

Learn more: brainly.com/question/13549064

Which triangles are similar A or b? I need help.

Answers

Answer:

A!

Step-by-step explanation:

please help ill mark brainliest if correct​

Answers

The answer is A) (3.1, 2.2)

Answer:

A

Step-by-step explanation:

Given the 2 equations

y = 2x - 4 → (1)

2x + 4y = 15 → (2)

Substitute y = 2x - 4 into (2)

2x + 4(2x - 4) = 15 ← distribute and simplify left side

2x + 8x - 16 = 15

10x - 16 = 15 ( add 16 to both sides )

10x = 31 ( divide both sides by 10 )

x = 3.1

Substitute x = 3.1 into (1) and evaluate for y

y = 2(3.1) - 4 = 6.2 - 4 = 2.2

solution is (3.1, 2.2 ) → A

I can’t solve or bring myself to understand it :/ I’m having difficulties

Answers

Answer:

x = 50

Step-by-step explanation:

Since the output is 0, x^2 is 2500 but written differently.

Just take the square root of 2500, which is 50.

50^2 = 2500

2500 - 2500 = 0

A spinner can land on either red, blue, green, or yellow. You spin once.
Find the number of possible outcomes in the sample space.
Please show me how to solve this.

Answers

Answer:

You have a 25% chance on landing on any of the colors  

Step-by-step explanation:

You Look at all of the posible ways you can land on which is Red, Blue, Green, and Yellow there are four colors in the spinner if you divide the number of colors (4) and divide it by 100 you will get 25 and that is your answer

Considering it's concept, it is found that the number of outcomes in the sample space is of 25%. You have a 25% chance on landing on any of the colors  

What is the sample space of an experiment?

The sample space is the set that contains all possible outcomes for an experiment.

here, we have,

In this problem,

You Look at all of the possible ways you can land on which is Red, Blue, Green, and Yellow

there are four colors in the spinner

if you divide the number of colors (4) and divide it by 100

you will get 25 and that is your answer

Hence, Considering it's concept, it is found that the number of outcomes in the sample space is of 25%. You have a 25% chance on landing on any of the colors.

More can be learned about sample spaces at brainly.com/question/25861936

#SPJ3

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