Use the remainder theorem to determine the remainder. Then use the remainder to determine if the binomial is the factor of a polynomial. f(x) = x^3 + x^2 - 66x + 54 is divided by x + 9.
a. Remainder: 0; not a factor
b. Remainder: 0; yes a factor
c. Remainder: 270; not a factor
d. Reaminder:270; yes a factor

Answers

Answer 1

Answer:

b

Step-by-step explanation:

f(x) = x³ + x² - 66x + 54

= (x² - 8x + 6)(x + 9) + 0

=> the answer is b

Answer 2

Answer:

b

Step-by-step explanation:

If (x + h) is a divisor of f(x) then f(- h) = remainder

If f(- h) = 0 then (x + h) is a factor of f(x)

Here divisor is (x + 9) , then

f(- 9) = (- 9)³ + (- 9)² - 66(- 9) + 54

        = - 729 + 81 + 594 + 54

        = 0

Thus remainder is 0 and (x + 9) is a factor of f(x)


Related Questions

Need help with this now! Giving 100 points and brainliest to whoever can give the best answer to this with an explanation.
The graph represents the speed at which Pete’s marble travels. The speed of Stephano’s marble is represented by the equation f=2.25s, where f is the distance in feet and s is the time in seconds. Whose marble will reach the 6-foot mark sooner?

Answers

Answer:

Note. There is a mismatch between the graph and the equation

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

As per the graph, 6 ft is reached at 4 secondsThe graphed line is f = 1.5s

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

If we go by the equation, then:

f = 2.25s6 = 2.25ss = 6/.2,25s = 2.67 seconds

Find an equation in slope-intercept form of the line that has a slope -7 and passes through point A(-7, -2)
A. y = 7x - 51 B. y = -7x - 51 C. y = -7x + 51 D. y = 51x - 7

Answers

Answer:

slope(m)=change in y/change in x

-7=y-(-2)/x-(-7)

-7=y+2/x+7

-7(x+7)=y+2

-7x-49=y+2

-7x-49-2=y

-7x-51=y (B)

Find the area of this trapezoid. Be sure to include the correct unit in your answer.

Answers

I’m not completely sure but I think that’s it’s 50cm^2

Which of the following equations is written in factored form?
O y= 2x² + 3x – 8
o y= 3 (2 + 5) (2 – 2)
o y=-2(1 + 5)2 – 2
O y = 3.2 - 5
Need help please!!

Answers

Answer:

Option B is correct option.

Step-by-step explanation:

We need to identify equations written in factored form.

Factored form: A factored form of expression is an expression broken down into a product of its factors.

In the given options A, C and D we don't have product of factors.

Only option B consists of product of factors.

So, Option B is correct option.

Write each fraction in simplest form.
1) 4/8
2) 3/9
??
22
3) 9/12
??
4) 3/6
??

Answers

Step-by-step explanation:

1. 4/8=1/2

2.3/9=1/3

3.9/12=3/4

4.3/6=1/2

PLEASE PLEASE PLEASE HELP I WILL GIVE XTRA POINTS AND BRAINALIST TO FIRST PERSON

Answers

Answer:

the answer is A because it has all numbers less than 15

Step-by-step explanation:

The cake store is having a 25 percent off sale on all of its cakes. If the cake you want reguarly cost 9$, how much would you save with the discount?

Answers

6.75 is the answer hope it helps

7 (3 - 0.5k) 3k - 5​

Answers

Your answer is going to be 63k-10.5k square 2 -5

Step-by-step explanation:

63k -10.5k square 2-5 and you have you answer

The temperature drops 2°F every hour. Make a table and write an equation to represent the total temperature drop over time.

Answers

Whats the original temp? Is this the full question?

Selina has $50. She wants to buy some donuts which cost $2.80 each. How many donuts can she buy?

Answers

Answer:

50/2.80= 17

17 dounuts

if you use synthetic division for this polynomial: 3x^5-12x^4+12x^3+30x^2-39x-42. What would the answer be?

Answers

Answer : x^5 - 4x^4 +4x^3 + 10x^2 - 13x - 14

Explanation :

(3x^5-12x^4+12x^3+30x^2-39x-42)/3 = x^5 - 4x^4 +4x^3 + 10x^2 - 13x - 14

write 28 + 24 as a product of two factors using the GCF and the distributive property

Answers

Answer:

4 x 13

Step-by-step explanation:

GCD of 28 and 24 is 4

28 = 4 x 7

24 = 4 x 6

u take the 4 out

4 (7 + 6)

4 x 13

The product of two factors using the GCF and the distributive property is 4(13).

What is the meaning of the greatest common divisor/factor?

The largest integer of highest degree that is an exact divisor of each of two or more integers.

The greatest common divisor of 24 and 28

24=2×2×2×3

28=2×2×7

We can see that the 2 and 2 is common in 24 and 28

The GCD of 28 and 24 is=2×2= 4

For the distributive property we have

28 = 4 x 7

24 = 4 x 6

we take the 4 out

4 (7 + 6)

=4 x 13

Therefore the GCD is 4 and by distributive property product is 4(13).

To learn more about the product visit:

https://brainly.com/question/10873737

2/3y + 3/4 = 8/9

help

Answers

Answer:

y = 5/24

Step-by-step explanation:

2/3 = 24/36

3/4 = 27/36

8/9 = 32/36

32-27 = 5

5/36 / 2/3 = 15/72 = 5/24

Answer:y=5/13

Step-by-step explanation:

8/9-3/4 is 5/36

divide by 2/3 is

I need this answer ASAP!!!!!!
What is 1 + 2?

Answers

Ummmmmm I think it’s 12

Answer:

3

Step-by-step explanation:

to increase an amount by 19% multiple by?

Answers

To increase an amount by 19% you need to multiple the amount by 1.19

Answer:

1.19

Step-by-step explanation:

The original full amount is 100%.

When you increase the full amount by 19%, you add 19% of the full amount to the full amount, so now you have 119%.

To find 119% of an amount, multiply he amount by 1.19 since 119% = 1.19

Answer: 1.19

Shel bought a $6,000 desk based on her income she can only afford to pay 600 per month The charge on the unpaid balance is 2% each month Calculate the balance outstanding at the end of month 2

Answers

Answer:

$5,030.40

Step-by-step explanation:

The balance outstanding at the end of any month is the due amount after adjusting for interest and loan repayment amount. The amount outstanding can be calculated as:

First month

Due amount = $6,000

Interest at 2% = $6,000*2% = $120

Loan repayment = $600

Reduction in balance = $600 - $120 = $480

Balance remaining = $6,000 - $480 = $5,520

Second month

Due amount = $5,520

Interest at 2% = $5,520*2% = $110.4

Loan repayment = $600

Reduction in balance = $600 - $110.4 = $489.60

Balance remaining = $5,520 - $489.60 = $5030.40

Hence, the balance outstanding at the end of month 2 is $5,030.40

please help me in math ​

Answers

there are two ways you can do this. Go through each of the nth terms separately and find the one that matches or you can find the nth term with the sequence itself.

so you find the size difference inbetween each term which is -5 so you know there will be -5n in your formula so then you need to make n= 1 (for the first term) so that equals -5 but you want -3 so you need to find what + -5 equals -3 which is 2.

So now you know your answer is 2-5n

someone please help​

Answers

Answer:A

Step-by-step explanation:

Answer:

Most likely A.

Step-by-step explanation: I'm guessing, but kinda makes sense because since there are 76 parking spaces, the probability will be decently low  

Shelly's Boutique had a Labor Day sale featuring 25% off any item. Tammy wanted to buy a blouse that originally sold for $21.99. To the nearest cent, how much will it cost her before tax to buy the blouse during the sale?

Answers

Given:

Original price of a blouse = $21.99

Sale = 25% off

To find:

The cost of blouse during the same before tax.

Solution:

Since Shelly's Boutique had a Labor Day sale featuring 25% off any item. It means price of each item in sale is 25% less than the original price.

[tex]\text{Price of blouse during sale}=21.99-25\%\text{ of } 21.99[/tex]

[tex]\text{Price of blouse during sale}=21.99-\dfrac{25}{100}\times 21.99[/tex]

[tex]\text{Price of blouse during sale}=21.99-0.25\times 21.99[/tex]

[tex]\text{Price of blouse during sale}=21.99-5.4975[/tex]

[tex]\text{Price of blouse during sale}=16.4925[/tex]

Approximate the value to the nearest cent (2 decimal places).

[tex]\text{Price of blouse during sale}\approx 16.49[/tex]

Therefore, the cost of blouse during sale is $16.49.

Answer:

16.49

Step-by-step explanation:

A 4-cup container of disinfectant costs $4.68. What is the price per pint?
$
Submit

Answers

1.17 is the answer. Divide 4.78 by 4.

I spent $120 shopping for food last week. This week I spent 12% more.
Which expression could be used to find how much I spent on food this
week?

Answers

Answer:

$120*.12= then add the answer to the money amount

Step-by-step explanation:

Answer:  120*1.12

The multiplier 1.12 represents the idea of increasing by 12%

This is because 100% + 12% = 1 + 0.12 = 1.12

For example, if you spend $100 this week and increase that by 12%, then you'll spend 100*1.12 = 112 dollars next week. Note how 12% of 100 is 12, which is the amount the budget goes up.

Which graph displays a directly proportional relationship?

Answers

Answer:

top graph

Step-by-step explanation:

The graph of a proportional relationship is a straight line passing through the origin.

The only straight line graph passing through the origin is the top one

The graph on option A displays a proportional relationship.

Option A is the correct answer.

What is an equation of a line?

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line on the graph is given as:

y = mx + c ____(1)

The graph on option A.

If the equation of a line is y = mx and the slope is a unit rate the graph shows proportional relationships.

We will select two points on the graph.

i.e

(2, 2) = (a, b) and (3.3) = (c, d)

Slope:

m = (d - b) / (c - a) = 3 - 2 / 3 - 2 = 1 / 1 = 1

Let (2, 2) = (x, y) and putting in (1) we get,

2 = 1 x 2 + c

2 = 2 + c

c = 2 - 2 = 0

c = 0

The slope of the line is 1

The equation of the line is y = x

Thus,

The graph displays a proportional relationship.

Option A is the correct answer.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ2

a b c d ?? help me pleas and ty

Answers

Answer:

a

Step-by-step explanation:

Answer:

a is the answer hopw this helps

HELP PLEASE
in order!!!

Answers

Answer:

m<6=54 m<4=126

Step-by-step explanation:

Will give brainiest
Surds
Step by step explanation please on this question
Make sure to use Surds

Answers

Answer:

3

Step-by-step explanation:

You need to multiple 3 by 3 because 3 has an exponent. That makes the 3 into a 9. the square root of 9 is 3 so the answer is 3

Find three consecutive even integers suche
that one half of their sum is between 15
and 21.

Answers

9514 1404 393

Answer:

  10, 12, 14   and maybe {8, 10, 12} and {12, 14, 16}, depending on the meaning of the question

Step-by-step explanation:

If x is the middle one, then their sum is 3x. You want ...

  15 < 3x/2 < 21 . . . . assuming "between 15 and 21" does not include 15 or 21

  30 < 3x < 42

  10 < x < 14

The only even integer in that range is 12, so the three integers are ...

  10, 12, 14 . . . . . half their sum is 18

__

We have used <, rather than ≤ in the above solution. This assumes that "between" does not include the values at the end of the range. If those values are included, then two additional solutions are possible: {8, 10, 12} and {12, 14, 16}. For the first set, the half-sum is 15; for the second set, the half-sum is 21.

Write the equation in point-slope form
of the line that passes through the point
(4, -7) and has a slope of -1/4.

Answers

Answer:

first i know but idk then

Find the value of x that makes m ∥ n .

Answers

Answer:

60

Step-by-step explanation:

(2x+15)=135    They're corresponding angles so they equal/congruent

     -15   -15       Subtract 15 on both sides since you're looking for x

2x = 120       Bring down the remains and subtract 135 from 15

 2        2        Add 2 on both sides

x= 60            Divide.

A student has some $1 and $5 bills in his wallet. he has a total of 15 bills that are worth $51. How much of each type of bill does he have?

Answers

Answer:

# of 5 dollar bills: 9

# of 1 dollar bills: 6

Step-by-step explanation:

9•5 = 45

1•6 = 6

To Check: 45 + 6=51

9 $5 bills and 6 $1 bills

Tickets to a baseball game cost $22 each and parking costs $10. What is the equation of the line that represents the cost of attending the game?
y-22=10x y=22x-10 y=22x+10 22x+y=10

Answers

The equation of the line is Y =22x + 10
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