Given p(x) = x4 – 13x2 – 25x – 12.

A) Use long division to determine the remainder when p(x) is divided by (x2 – 4)? Show all of your work for full credit.

B) Use mathematical methods to prove that your quotient and remainder are correct. Show all of your work for full credit.

Answers

Answer 1

Answer:

Below.

Step-by-step explanation:

p(x) = x^4 - 13x^2 – 25x – 12

Long division:

x^2 - 4)x^4 - 13x^2 – 25x – 12( x^2 - 9  <-------- Quotient

           x^4 -  4x^2

Subtract:       -9x^2 -  25x

                     -9x^2  + 36

                                 -25x - 36 - 12

So the remainder is -25x - 48 (Answer).

B)   If the above are correct then:

(x^2 - 4) * quotient + remainder  = the original form of  p(x).

(x^2 - 4)(x^2 -9)  - 25x - 48 = the original p(x).

p(x) = x^4 - 9x^2 - 4x^2 + 36  - 25x - 48

= x^4 - 13x^2 - 25x -12 = original p(x)

                   


Related Questions

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[tex]\\ \sf\longmapsto x+47>36[/tex]

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Graph attached

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Answer:

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Answer:

Step-by-step explanation:

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Step-by-step explanation:

the slope is the ratio of "y coordinate change / x coordinate change".

so, in our case here

x changes by +2 (from 1 to 3).

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Answer: 6 in.

Step-by-step explanation:



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Answer:

2.35

Step-by-step explanation:

2 x 2 eqaul 9 times 2

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Step-by-step explanation:

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Read Fred's conclusion. If the sum of the digits of a number is a multiple of 3. then the number is a multiple of 6. Which statement best summarizes Fred's conclusion? The conclusion is true.

A .The number 42 is an example The conclusion is true.
B There are no counterexamples The is false.
C There are no counterexamples. The conclusion is false.
D The number 45 is a counterexample​

Answers

Answer:

the answer would be a because 42÷6=7 and 42÷3=14.

The correct answer is option A) The number 42 is an example The conclusion is true.

42 is a multiple of both 3 and 6.

How many does multiple mean?

Containing more than once, or more than one; consisting of more than one; manifold; repeated many times; having several, or many, parts.

What is a multiple in math?

A multiple in math is the number you get when you multiply a certain number by an integer. For example, multiples of 5 are: 10, 15, 20, 25, 30…etc. Multiples of 7 are: 14, 21, 28, 35, 42, 49…etc.

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Answers

Answer:

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Step-by-step explanation:

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You go to a restaurant and get a bill for $95. You need to tip the waitress. The service was good so you decide on tipping the waitress 20%. What is the tip that the waitress will receive

Answers

Answer:

19 dollars.

Step-by-step explanation:

0.20 x $95.00=$19.00.

19 dollars because 20% of 95 is 19. You can find this by doing 20% (or 0.2) times 95 :)

Which graph shows Point P as (–5,6) and Point Q as (3,–4)?

Answers

hich graph shows Point P as (–5,6) and Point Q as (3,–4)?

Kevin and Randy Muise have a jar containing 32 ​coins, all of which are either quarters or nickels. The total value of the coins in the jar is ​$5.40. How many of each type of coin do they​ have?
PLSSSS AnSWER QUICKLY

Answers

Answer:

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Step-by-step explanation:

You have 32 coins in your pocket consisting of nickels and quarters with a total value of $5.40

How many nickels and quarters do you have?

Step 1: Setup Coin Value and Coin Total Equation:

Coin Value Equation → 0.05n + 0.25q = $5.40 where n = nickels and q = quarters

Coin Total Equation → n + q = 32

Step 2: Rearrange Coin Total Equation in terms of nickels (n)

n = 32 - q ← Revised Coin Total Equation

Step 3: Plug in our Revised Coin Total Equation for n into our Coin Value Equation:

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Step 4: Subtract 1.6 from each side of the equation to isolate q

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0.2q = 3.8

Step 5: Divide each side of the equation by 0.2 to isolate q

0.2q

0.2

=

3.8

0.2

q = 19

Step 6: Using our value for q, Solve for n using our Coin Total Equation:

n + 19 = 32

Subtracting 19 from both sides, we get n + 19 - 19 = 32 - 19

n = 13

Summarizing our word problem, we see that 19 quarters and 13 nickels adds up to $5.40

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a) o
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Answers

Answer:

i think d) -25 is answer

Step-by-step explanation:

good luck

Answer:

d) -25

Step-by-step explanation:

Because -25 is less than -23 . as it is negative integers

Based on the scatterplot, what is the best prediction of the amount of $ in sales when the temperature is at 21°C?​

Answers

Answer:

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Step-by-step explanation:

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Answer:

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(Step-by-step explanation:

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Answers

Answer:

2, 4, 5, 6, 7, 8

Step-by-step explanation:

The number 2 is not a factor of 9. The correct option is D.

What is factor?

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

The given number is 9.

To find the factor of 9:

Number m that evenly divides another number 9.

In simple words, when we divide the number 9 by a number m.

We should get a whole number.

From the options,

9/1 = 9

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9/9 = 1

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To learn more about the factor;

https://brainly.com/question/18187355

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The complete question is:

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Answer:

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Step-by-step explanation:

E

Directions: Compare the sides and angles by filling in the blank with a < or > symbol.

Answers

The correct comparison as shown in the figures are:

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From the given diagram, we are to fill in the blank spaces with a < or > symbol.

21) The measure of the angles is a function of the measure of the sides.

Since the angle facing the side QR is less than that of QS, hence QR < QS

22) Similarly for this figure, the angle facing the side AB is greater than that of CD, hence AB >  CD

23) Also, for this figure, the side facing the angle m<FJG is greater than the side facing the angle m<HJG, hence m<FJG > m<HJG

24) Also, for this figure, the side facing the angle m<QSP is greater than the side facing the angle m<QSR, hence m<QSP > m<QSR

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Which of the following sequences below is a Geometric Sequence?
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B. 1, 3, 9, 27

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What is the answer to 1010 + 0101? (Binary) *​

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Answer:

1111 is the answer to your question.

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Answers

Using the slope of the linear function, it is found that:

The slope is of 0.5, which means that the plant grows by 0.5 inches each day.

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

m is the slope, which is by how much the output y changes when the input x changes by 1.b is the y-intercept, which is the value of y when x = 0.

In this problem:

x is the time in days.y is the height in inches.

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Then, applying the interpretation:

The slope is of 0.5, which means that the plant grows by 0.5 inches each day.

To learn more about slopes and linear functions, you can take a look at https://brainly.com/question/16302622

Answer:

hes correct. the slope is 0.5 and it grows 0.5 inches everyday

Step-by-step explanation:

TE Irene has a collection of 32 dolls that have either blue eyes or green eyes. She has 14 more green-eyed dolls than blue-eyed dolls. How many dolls of each type does Irene have? Let x represent the number of green-eyed dolls. Let y represent the number of blue-eyed dolls.​

Answers

The formula

x + y = 32

Find our X value

y + 14 = x

Sub for x

(y + 14) + y = 32

Remove Parathesis

y + 14 + y = 32

Add

2y + 14 = 32

Subtract

2y = 18

Divide

y = 9

Sub for y

x + 9 = 32

Subtract

x = 23

Double Check:

9 + 14 = 23

23 + 9 = 32

I hope this helps! :)

The verticles of a triangle are the points R(3,c),Q(9,2) and R(3c,11) where c is constant. Given that angle PQR is 90​

Answers

Answer:

Step-by-step explanation:

Find c if ∠PQR = 90°?

I will ASSUME you mean point P is at (3. c)

slope of PQ is (2 - c) / (9 - 3) = (2 - c) / 6

slope of QR is (11 - 2) / (3c - 9) = 9 / (3c - 9)

perpendicular lines have negative reciprocal slopes.

(2 - c) / 6 = -1(3c - 9)/9

9(2 - c) = -6(3c - 9)

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1) f(4) = g(4)
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3) f(2) = g(-2)
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Answers

Answer: 4)

Step-by-step explanation:

f(4) = -14

g(4) = 10

g(-2) = 4

f(2) = -8

f(-2) = 4

The correct statement is 4) f(-2) = g(-2)

Or by inspection, we can see that the graph f(x) intersects g(x) at x = -2 and    y = 4. So, f(-2) = g(-2) = 4 is true

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