The polynomial x^4+px^3+qx^2+rx+6 is exactly divisible by each of (x-1), (x-2) and (x-3).
Find the values of p, q and r.

Answers

Answer 1

The remainder theorem says that a polynomial f(x) has a remainder of f(c) upon getting divided by x - c. So if

f(x) = x⁴ + p x³ + q x² + r x + 6

is divisible by x - 1, x - 2, and x - 3, then we have

f (1) = 7 + p + q + r = 0

f (2) = 22 + 8p + 4q + 2r = 0

f (3) = 87 + 27p + 9q + 3r = 0

Solve the system for p, q, r. You can eliminate r by substituting the first equation into the other two:

p + q + r = -7

8p + 4q + 2r = -22   →   6p + 2q - 14 = -22   →   3p + q = -4

27p + 9q + 3r = -87   →   24p + 6q - 21 = -87   →   4p + q = -11

Eliminate q by adding (-1) times the first equation to the second one, then solve for p :

- (3p + q) + (4p + q) = - (-4) + (-11)

-3p - q + 4p + q = 4 - 11

p = -7

Solve for q :

3p + q = -4   →   3 (-7) + q = -4   →   q = 17

Solve for r :

p + q + r = -7   →   -7 + 17 + r = -7   →   r = -17


Related Questions

Which is equal to 7√3 ?


7^3


21


(13)^7


7 1/3

Answers

Step-by-step explanation:

D is the correct answer of this question ....

Collect like terms
2y - y​

Answers

Answer:

The answer is y

Step-by-step explanation:

2y−y

=2y−1y

=2y+−1y

=y+y+−y

=y

If anyone knows the answer please help!

Answers

You’re answer would be B

i. After how many weeks will Jennifer and William have the same amount of money in their bank accounts?



ii. How much will be in their accounts?

Answers

Answer:

5 weeks$100

Step-by-step explanation:

Part i

Jennifer's account:

f(x) = 10x + 50

William's account can be expressed as:

g(x) = 14x + 30

Because the rate of change is 14 and y-intercept is 30

They will be same after x years, f(x) = g(x)

10x + 50 = 14x + 3014x - 10x = 50 - 304x = 20x = 5

The accounts will be same after 5 weeks

Part ii

The amount in the accounts after 5 weeks:

f(5) = g(5) = 10*5 + 50 = $100

Answer:

5 weeks

Step-by-step explanation:

Find the equation of willam's account:

1. find rate x1-x2

44-30      plug in

14 =rate  30=y-intercept     starting valuse is always intercept

44+14=58       check

f(x)= 10x+50

f(x)= 14x+30     solve

10x+50=14x+30   set values together

20=4x        subtract 10x and 30 from both sides

x=5

Algebra - Two Questions
1. A system of linear equations is shown​ below as well as the first steps that Raffi is using to solve this system of linear equations by substitution. Choose the statement that best describes how Raffi is progressing toward a solution.

7x+y=4

3x−2y=3

Solution: Solve the first equation to obtain y=−7x+4. Substitute this into the second equation to get 3x−2⋅−7x+4=3.


2. Solve the following system by the substitution method.

2x−y=−4

−5x+3y=14

Answers

Answer:

The answer is below

Step-by-step explanation:

1) Below are the linear equations.

7x+y=4         (1)

3x−2y=3      (2)

The above linear equations are a system of equations. The substitution method is a technique for solving systems of linear equations.

Given that:

7x + y = 4

y = 4 - 7x

substitute y = 4 - 7x in equation 2, hence:

3x - 2(4 - 7x) = 3

3x - 8 + 14x = 3

17x = 3 + 8

17x = 11

x = 11/17

Put x = 11/17 in y = 4 - 7x

y = 4 - 7(11/17)

y = -9/17

2) 2x−y=−4     (1)

 

−5x+3y=14     (2)

From equation 1:

2x−y=−4

y = 2x + 4

Put y = 2x + 4 in equation 2:

-5x + 3(2x + 4)  = 14

-5x + 6x + 12 = 14

x + 12 = 14

x = 2

Put x = 2 in y = 2x + 4:

y = 2(2) + 4

y = 8

Answer:

1. Raffi forgot to place the substituted expression in parentheses.

2. (2, 8)

Step-by-step explanation:

If you are taking the Solving Systems With Substitution Quick Check from Connexus here are all of the answers:

1. Solve one linear function in terms of one of its variables.

2. Substitute 3y from the second equation for x in the first equation.

3. Raffi forgot to place the substituted expression in parentheses.

4. Yes, because substituting the given ordered pair yields two true expressions.

5. (2, 8)

multiplicaiton problem where both factors are fractions and the product is less than the factors ANSWER NOW PLEASE

Answers

Answer:

There is no question attached.

Step-by-step explanation:

Answer:

1/5 * 1/2 = 1/10

Step-by-step explanation:

Choose any two factor fractions less than 1. The result (product) will be necessarily smaller than each of the factors. Above answer is an example

1/5 * 1/2 = 1/10, where it is clear that

1/10 < 1/5 and

1/10 < 1/2

Gianna has 20 cookies in a bag. 20% of the cookies are vanilla. How many cookies are vanilla?

Answers

Answer:

4 cookies are vanilla

Step-by-step explanation:

because 20% is technically 1/5th of 100% we need to divide 20 by 5

20/5 = 4

somebody help.. im so lost!!

Answers

what type of math is this?

Pls pick one option to help me out

Answers

option is c=2/3

2/3+ 1/7 = 17/21

Best answer gets brainliest hurry ASAP

Answers

Answer:

its b

Step-by-step explanation:

mark as brainliest plz im right

Answer:

b

Step-by-step explanation:

the ratio answer is b.

What is the slope of the line?

Answers

Answer:

-1

Step-by-step explanation:

Remember, slope is rise/run

Start from a point on the line and count up and over until you reach another point on the line.

For example, start from (0,-2), count up and left until you get to (-2,0). This gets you 2/2, which reduces to 1.

Since the line represents a negative slope, the slope is -1.

If it takes 9 3/4 yards of material to make curtains for 3 windows, how much material is needed?

Answers

Answer:

3.25 yards of materials will be needed for 1 window

Answer:

3 1/4 (Verified) ✅

Step-by-step explanation:

This is a rate problem, so we will write rate as a proportion and write the desired rate with x for the unknown value we need to find.

9.75/3 = x/1

Cross-mulitply

3x = 9.75

Divide by 3

x = 3.25 or 3 1/4

Another great thing with proportions is that we can check them to ensure we got the correct answer. All we do is substitute our determined value in for x

9.75/3 = 3.25/1

9.75 = 9.75 ✅

The answer of x = 3 1/4 is correct.

Find me the point please

Answers

Answer:

(-2,-3)

Step-by-step explanation:

if you eat 4 medium strawberries you get 48% of your daily recommended amount of vitamin c what fraction of your daily amount of vitamin c do you still need

Answers

13/25 would be the smallest fraction you can get otherwise 52/100 if your teacher doesn’t want it reduced hope this helped

The scale of a map is 1 clear : 13 km. Find the actual distance corresponding to the map distance. The distance on the map is 4.5 cm The actual distance is ___ km

Answers

Answer: The actual distance is 58.5 km.

Step-by-step explanation:

Given:  Scale of map = 1 cm : 13 km

The distance on the map is 4.5 cm.

To find : The actual distance corresponding to the map distance.

The actual distance corresponding to the map distance =

( distance on the map)  x ([tex]\dfrac{13}{1}[/tex])

[tex]=4.5\times13\\\\=58.5\ km[/tex]

Therefore , the actual distance is 58.5 km.

150% of 150 is what number? (15 points I think?)

Answers

225 percent

Step-by-step explanation:

150 is the whole and 150 divided by 150 is 1.

1 whole is 100 percent

Answer:

225 will be correct

Step-by-step explanation:

Mrs. Williams combined 3 ½ cups of peat moss, 5 ¼ cups of compost , and 6 ¾ cups of fertilizer to make plant food for her roses. She evenly distributed the plant food among 4 rose bushes. How many cups of plant food were used for each rose bush?

Answers

Answer:

3 7/8 cups plants food

Step-by-step explanation:

peat moss = 3 ½ cups

compost = 5 ¼ cups

fertilizer = 6 ¾ cups

Total mixture = peat moss + compost + fertilizer

= 3 ½ cups + 5 ¼ cups + 6 ¾ cups

= 7/2 + 21/4 + 27/4

= 14+21+27/4

= 62/4

Total mixture = 62/4 cups

She evenly distributed the plant food among 4 rose bushes

Each rose bush uses = Total mixture / number of rose bushes

= 62/4 ÷ 4

= 62/4 × 1/4

= 62/16

= 3 14/16

= 3 7/8 cups plants food

Each rose bush uses = 3 7/8 cups of plants food

Which describes the correct way to convert minutes to hours?
Divide the number of minutes by 24.
Multiply the number of minutes by 24.
Divide the number of minutes by 60.
Multiply the number of minutes by 60.

Answers

Answer:

Divide the number of minutes by 60.

Step-by-step explanation:

Solve this system of linear equations. Separate
the x- and y-values with a comma.
16x = 84 - 2y
14x = 72 - 2y

Answers

Answer:

6x = 84 - 2y

14x = 72 - 2y

Step-by-step explanation:

Which figure has line symmetry?
O A.
F
O B.
H
O C.
J
O D.
L
O E.

R

Answers

Answer:

??????

Step-by-step explanation:

Answer:

???

Step-by-step explanation:

A new health drink has 150​% of the recommended daily allowance​ (RDA) for a certain vitamin. The RDA for this vitamin is 50 mg. How many milligrams of the vitamin are in the​ drink? There are nothing mg of the vitamin in the drink.

Answers

Answer:

the number of milligrams of the vitamin in the drink is 75 mg

Step-by-step explanation:

The computation of the number of milligrams of the vitamin in the drink is as follows:

= RDA of the vitamin × given percentage ÷ percentage

= 50 mg × 150 ÷ 100

= 75 mg

hence, the number of milligrams of the vitamin in the drink is 75 mg

We simply applied the above formula so that the correct value could come

And, the same is to be considered

What is absolute value?


The distance a number is from O on a number
line.

The Additive Inverse Property

The opposite of a number

Answers

Answer:

the distance a number did from 0 onna number line

hey guys please answer if you know​

Answers

Answer:

19

Step-by-step explanation:

note that

(a + b)² = a² + b² + 2ab , that is

a² + b² + 2ab = (a + b)² ← subtract 2ab from both sides

a² + b² = (a + b)² - 2ab

           = 5² - 2(3)

           = 25 - 6

          = 19

Answer:

19

Step-by-step explanation:

since value of both a+b and a*b are given

formula for a^2 + b^2 is (a+b)^2-2*a*b

Substituting those value,

a^2+b^2=5^2-2*3

i.e. 25-6

=19

Si sen A = 7/25 donde "A" pertenece al segundo cuadrante y el cos B = -4/5 donde "B" pertenece al segundo cuadrante Calcular cosec(A).cos(B).tan(A).cot(B)

Answers

Not sure just need answers because I don’t no the answers

which expression can be used to determine the slope of the line that passes through the points (-7,3) and (1, -9)?

1. 1-(-7)/-9-3
2. 1+(-7)/-9+3
3. -9-3/1-(-7)
4. -9+3/1+(-7)​

Answers

Answer:

-9-3/1--7

Step-by-step explanation:

gradient (m) =-9-3/1--7

m =-12/8

Solve this equation.
Y/4-4=5 y=

Answers

Answer:

16/19

Step-by-step explanation:

Hi I need to figure if this is a function?

Answers

Answer:

no it is not a function

Step-by-step explanation:

function- for every input there is only one output

(1,7),(2,13),(3,13) it has two 13 so it is not a function

Round 9 1/3 to the nearest whole number

Answers

Answer:

Nearest Whole Number: 9

Step-by-step explanation:

Answer:

im guessing it would just be 9

Step-by-step explanation:

because its 1 out of three so that leaves two so its closest to 9

Find the inverse of Y=2x-6

Answers

Answer:

Step-by-step explanation:

f^-1(x)=x/2+3


To find the inverse, interchange the variables and solve for
y
y
.
f

1
(
x
)
=
x
2
+
3

What is the percent Of decrease from 50 to 21

Please anwser accurate and I give brailiest

Answers

Answer:

29%

Step-by-step explanation:

To find the decrease from 50 to 21 you would subtract 50 - 21. You get 29. This is the same as 29/100. 29/100 is also 0.29 or 29%.

Hope it helps! (I'm so sorry if it's incorrect).

Answer:

57.9% please give me brainliest i used a percentage calculator :)))

Step-by-step explanation:

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