Express f(x) in the form f(x) = (x - k)q(x) +r for the given value of k.
f(x) = 4x^3+ x² + x-8, k= -1

Answers

Answer 1

Answer:

f(x) = (x + 1)*(4*x² - 3*x + 4) - 12

Step-by-step explanation:

We have:

f(x) = 4*x³ + x² + x - 8

We want to write this in:

f(x) = (x - k)*q(x) + r.

with k = -1

Then we want to write:

4*x³ + x² + x - 8 = (x - (-1))*q(x) + r

4*x³ + x² + x - 8 = (x + 1)*q(x) + r

Because f(x) is polynomial of degree 3, we know that q(x) must be a polynomial of degree 2.

then:

q(x) = a*x² + b*x + c

Then:

4*x³ + x² + x - 8 = (x + 1)*(a*x² + b*x + c) + r

4*x³ + x² + x - 8 = a*x³ + b*x² + c*x   + a*x² + b*x + c + r

if we take common factors in the right side we get:

4*x³ + x² + x - 8 = a*x³ + (b + a)*x² + (c + b)*x + (c + r)

Now, we must have:

4*x³ = a*x³

then:

4 = a

We also must have:

x² = (b + a)*x²

1 = (b + 4)

1 - 4 = b

-3 = b

We also must have:

x = (c + b)*x

1 = (c + (-3))

1 + 3 = c

4 = c

And finally:

- 8 =  (c + r)

-8 = 4 + r

-8 - 4 = r

-12 = r

Then:

f(x) = (x + 1)*(4*x² - 3*x + 4) - 12


Related Questions

Alex's pig weighs under 220 pounds.
Let p = the weight of the pig

Answers

Answer:

p > 220

Explanation:

This inequality says, "p (the weight of the pig) is less than 220." This describes the situation shown. So, the answer is p > 220.

Good luck ^^

solve 7!!!!!!!!!!!!!!!!!!!!!!!

Answers

ummmmm what? Is this a troll or something

Answer:

?

Step-by-step explanation:

y=((3x+1)³)-², find dy/dx​

Answers

Firstly simplify then differentiate

A pair of shoes that normally sells for $85.00 goes on sale for 35% off. Season thinks that the sale price should be $50.00 but Melanie disagrees and says the price should be $55.25. Aiyanna says they are both wrong and decides the price should be $29.75. Who is correct and why?

Answers

Answer:

Melanie is correct

Step-by-step explanation:

35% of 85 is 29.75 so take that away from the original price and you get 55.25

This means the price will be 55.25$

Answer:

Melanie is correct since 65% of $85.00 is $55.25.

Step-by-step explanation:

The original price of the shoes is $85.00. That is 100% of the price of the shoes since 100% is a whole amount.

The discount on the shoes is 35%.

100% - 35% = 65%

That means the sale price is 65% of the original price. Now we calculate 65% of $85.00.

65% of $85.00 =

= 0.65 * $85.00

= $55.25

Answer: Melanie is correct since 65% of $85.00 is 55.25.

The ___ is the ratio of a length of the new figure to the corresponding length on the original figure

Answers

Answer:
scale factor

Explanation:
The ratio of the side lengths of the image to the corresponding side lengths of the original figure is the scale factor of the dilation.

Determine the equation of a circle with center at (8, 10) and radius is 6​

Answers

Use the equation ( x - h ) ^ 2 + ( y - k ) ^2 = r ^2
Where (h,k) is the center and the r is the radius . So the equation is as follows
( x- 8 ) ^2 + ( y -10 ) ^ 2 = 6^2

Hope this helped

Drag each tile to the table to multiply
(6x – y)(2x – y + 2).

Answers

fill the table

2x -y 2

6x 12^2 -6xy 12x

-y -2xy y^2 -2y

Need help with this if possible ​

Answers

Answer:

hope it helps...

Step-by-step explanation:

Please help, brainliest for correct answer

Answers

Answer:

11494.04 units

Step-by-step explanation:

V = 4/3 [tex]\pi[/tex] r³ = 4/3 · [tex]\pi[/tex] · 14³ ≈ 11494.04032

17% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who

favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight

(a) P(3)=(Round to three decimal places as needed)

(b) P(x24) =(Round to three decimal places as needed.)

(c) P(x<8)=(Round to three decimal places as needed.)

Answers

Answer:

Following are the solution to these question:

Step-by-step explanation:

Following are the binomial distribution with parameters:

[tex]n = 12\\\\p = 0.24[/tex]

For point a:

[tex]\to P(X = 3) = binom.dist(3, 12, 0.24, False) = 0.2573[/tex]

For point b:

[tex]\to P(X > 4) = 1 - P(X < 3) = 1 - binom.dist(3, 12, 0.24, True) = 0.3205[/tex]

For point c:

[tex]\to P(<8) = binom.dist(7, 12, 0.24, True) = 0.9979[/tex]

A box of cherries weighs 2 1/4 pounds.
If you bought 5 boxes, what is the total
weight of the purchased cherries?

Answers

Answer:

The total weight of the purchased cherries is [tex]11\frac{1}{4}[/tex] pounds.

Step-by-step explanation:

Multiply [tex]2\frac{1}{4}[/tex] by 5.

[tex]2\frac{1}{4} * 5 = 11 \frac{1}{4}[/tex]

Answer:

11.25 or 45/4

Step-by-step explanation:

2 1/4 times 5

Cellular phone service is available for $37 per month for 1847 minutes. What is the monthly cost per minute? Round your answer to the nearest tenth of a cent.

The cost for the phone service is cents per minute.

Answers

The cost per minute is .02 cents

from 2005 to 2015, a population of lions decreased by 2% annualy. there were 1500 of this population of likns in 2005. how many lions wew left by 2015

Answers

Answer:

30

Step-by-step explanation:

I think that's the answer but if I'm wrong tell me right away I'll try another method.

Find the limit when X approaches zero
2xsinx/1-cosx

Answers

Answer:

4

Step-by-step explanation:

[tex] Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x} [/tex]

[tex] =Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x}\times \frac{1+\cos x}{1+\cos x} [/tex]

[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{1^2 -\cos^2 x} [/tex]

[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{1 -\cos^2 x} [/tex]

[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{sin^2 x} [/tex]

[tex] =Lim_{x \to 0}\frac{2x(1+\cos x) }{sin x} [/tex]

[tex] =Lim_{x \to 0} 2(1+\cos x) \times \frac{1}{Lim_{x \to 0}\frac{sin x}{x}} [/tex]

[tex] =2(1+\cos 0) \times 1 [/tex]

[tex] = 2(1+1) [/tex]

[tex] = 2(2) [/tex]

[tex] \therefore Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x}= 4 [/tex]

if we use the quadratic expression below to complete a diamond, what value will go at every bottom of the diamond

a. -4
b. 4
c. 1
d. 5​

Answers

Answer:

if we use the quadratic expression below to complete a diamond, what value will go at every bottom of the diamond

is -4

Answer:

if we use the quadratic expression below to complete a diamond, what value will go at every bottom of the diamond

its 1 because

1. Kathy is building a bed for her dollhouse. She used her real bed as a guide for how to
create the dollhouse bed. Her bed is 36 inches wide and 60 inches long. If she wants
to scale this down by 1/10, what would be the dimensions of the dollhouse bed?
Explain how you got your answer.
*Use the term SCALE FACTOR in your explanation.


PLS ANSWER QUICKLY !!!

Answers

The answer to the question is Ashby

Which temperature is warmer: -3 or -4 degrees Celsius?

Answers

Answer:

-3

Step-by-step explanation:

The answer of 4.38 x 10^4 in ordinary notation is

Answers

4,38 * 10⁴ = 4,38 * 10 000 = 43 800

At the time of her​ grandson's birth, a grandmother deposits $2000 in an account that pays 6.5% compounded monthly. What will be the value of the account at the​ child's twenty-first​ birthday, assuming that no other deposits or withdrawals are made during this​ period?

Answers

Answer:

$41, 863. 50

Step-by-step explanation:

$2000 - 6.5% = $1,993.50

$1,993.50 x 21 = $41, 863. 50

Solve for x.
3x - 4 = 2x - 10
O x = 6
OX= -6
OX= 14
O x=-14
Please help
Will give you brainly

Answers

Answer:

x = -6

Step-by-step explanation:

We have the equation 3x - 4 = 2x - 10 and are asked to find "x".

To solve , we need to get "x" alone entirely.

3x - 4 = 2x - 10

Subtract 2x from both sides :

x - 4 = -10

Add 4 to both sides to get our answer :

x = -6

Answer:

the answer is equal to-6

The length of a rectangular garden is 8m greater than twice the width the area of the garden is 280m^2 what is the width of the garden

Answers

Step-by-step explanation:

Given :-

The length of the garden 8m greater than 2 times the width.

Area of the garden is 280 m²

Let us consider the length as x and width as y.

Sp, we can day length as :-

x = 8 + 2y ---(1)

Now, we know that:-

Area of Rectangle = Length × Breadth

280 = x * y

We can replace the value of x now,

280 = y × ( 8 + 2y)

280 = 8y + 2y²

2y² + 8y - 280 = 0

y² + 4y - 140 = 0

Factorise it.

(y -10)(y + 14)

Cancelling -ve value, we get the width as 10 metres.

Hope it helps :)

Answer:

Step-by-step explanation:

Width = w

Length = 2w + 8

Area of rectangular garden = 280 square meter

length * width = 280

(2w + 8 ) *w = 280

2w * w + 8*w = 280

2w² + 8w = 280

2w² + 8w - 280 = 0

Divide the whole equation by 2

w² + 4w - 140 = 0      

w² + 14w - 10w - 14 *10 = 0

w(w + 14) - 10(w + 14) = 0

(w + 14)(w - 10)= 0

w - 10 = 0       {Ignore w + 14, as measurements will not be -ve}

w = 10 m

l = 2*10 +8

= 20 +8

l  = 28 m

For what values of b will F(x) = logbx be a decreasing function?

Answers

Answer:

It is a decreasing function for 0 < b < 1.

Step-by-step explanation:

Logarithm function:

The logarithm function is given by:

[tex]F(x) = \log_{b}{(x)}[/tex]

The base b determines if the function increases or decreases.

For 0 < b < 1, the function decreases.

For b > 1, the function increases.

In this question:

By the definition above, it is a decreasing function for 0 < b < 1.

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