Prove that when a polynomial function p(x) is divided by a first degree polynomial ax + b the remainder is p(-b/a)

Answers

Answer 1

Answer:

r = p(-b/a)

Step-by-step explanation:

Let p(x) = q(x)(ax + b) + r(x) where q(x) is the quotient when p(x) is divided by ax + b and r(x) is the remainder.

Since ax + b is a first degree polynomial, r(x) is one power less than ax + b is is just a constant, r.

So, p(x) = q(x)(ax + b) + r

Now, p(x) = r when q(x)(ax + b) = 0

since q(x) ≠ 0, ax + b = 0 ⇒ ax = -b ⇒ x = -b/a

⇒ p(x) = r when x = -b/a

So, r = p(-b/a)

So, the remainder when a polynomial function p(x) is divided by a first degree polynomial ax + b is p(-b/a)


Related Questions

Someone help and please make sure it’s right

Answers

A is the answer. Hope you finish the assignment

Answer:

20°

Step-by-step explanation:

Look at the attached photo.

∠a and ∠e are equal because they are vertical angles.

So, m∠a = 110°

Then, ∠f is an exterior angle to angles a and c. So,

m∠f = m∠a + m∠c

Substitute and solve.

130 = 110 + m∠c

m∠c = 20°

Then, ∠c and ∠d are vertical angles so they are equal.

m∠c = m∠d

m∠d = 20°

I hope this helps! Feel free to ask any questions!

PLEASE HELP I need to answer the question quick .

Write a linear equation in point-slope form for the line that goes through
(1, -3) and (3,9)

Answers

Answer:

D. y+3 = 6(x-1)

Step-by-step explanation:

i just wrote it out and i think thats the answer but not sure. hopefully this helps :)

Geometry Angle of elevation/depression

Answers

Answer:

m∠ACB = 49.88°

Step-by-step explanation:

From the figure attached,

Measure of wire AC attached to the top 'C' of the building BC = 340 m

Horizontal distance between the base 'B' of the building and point A = 260 m

Angle of depression = ∠ACB

By applying sine rule in the given triangle,

sin(∠ACB) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

                 = [tex]\frac{AB}{BC}[/tex]

                 = [tex]\frac{260}{340}[/tex]

m∠ACB = [tex]\text{sin}^{-1}(764706)[/tex]

             = 49.88°

I WILL GIVE BRAINLEST TO FIRST ANSWER!! DUE 20 MINUTES!!
Which expression is equivalent to 1-1/4+2/5
a, b, c, or d?

Answers

Answer:

D

Step-by-step explanation:

1 - 1/4 + 2/5 = 23/20

20/20 - 5/20 = 15/20

15/20 + 8/20 = 23/20

hope this helps! :)

i need help what is 2 and 7/8 + 2 and 7/8 + 2 and 7/8 =
i dont know i need help

Answers

Answer:

8 and 5/8

Step-by-step explanation:

calculator

Answer:

8.625

Step-by-step explanation:

hope this helps  :)

Point A is given on the coordinate plane

What will the coordinates of the point be after Point A is reflected across the y-axis ?


I tried it and I got
(4,-3)

But i am not sure ?
Help pls

Answers

Answer:

its (-4,3)

Step-by-step explanation:

Remmember U reflecting on y-axis

B/c reflecting on y axis only the x becomes negative

Brainliest??

Answer:

(-4 , 3)

Step-by-step explanation:

The y-axis is the vertical axis/line out of the two perpendicular lines.

Vertical line/axis (y-axis)=  │

Horizontal line/axis (x-axis)=  ___

When you reflect Point A, it will be reflected across the vertical line (y-axis). This means that the point will be on the left side in Quadrant II (- , +).

A scooter costs $160. A bicycle costs 20% more than the scooter. How much does the bicycle cost? ?​

Answers

Answer:

$192

Step-by-step explanation:

160 = 100% or 1.00

20% = 0.2 + 1.00

       =  1.20

160 x 1.20 = $192

Answer:

$192

Step-by-step explanation:

$160 + 20% = $192

32+4 X (16 X 1/2) -2

Answers

Answer: look at the picture

Step-by-step explanation: Hope this help :D

What is the volume of the triangular prism ? Please hurry

Answers

Answer:

576 is the answer

multiply all the numbers

9ftx4ftx16ft=576ft^3

How much vanilla extract will be needed to make 2 dozen cookies? Show your work.

Answers

Answer: the answer is 2 teaspoons of vanilla extract.

hope this helped

pls help on my homework. due tonight
i need help asap
Match the given graphs with the corresponding functions in the table below. Use the letter in the
bottom left corner of the graph.

b) Given the function ff(xx) = llllll3(xx + 2) − 1, state the following characteristics:

Asymptote:__________________ End Behavior: _______________________________________
_______________________________________

c) Describe what an asymptote is, and write the end behavior in your words.

Answers

Answer:

A line that a curve approaches as it heads towards infinity

The asymptote is -2 there is no end behavior

Step-by-step explanation:

5
Which line is parallel to the line y = -5/2x - 7

A) 2x + 5y = -5
B) 2x - 5y = 30
C) 5x + 2y = 4
D) 5x – 2y = 8

Answers

Answer:

The answer is C) 5x + 2y = 4

Step-by-step explanation:

Johnson’s Hardware randomly selects 125 of its customers and questions them to determine their overall customer satisfaction rating. The poll indicates 100 were completely satisfied, 15 were satisfied, and 10 were not satisfied at all. What percent of customers were either satisfied or completely satisfied? About how many of the 5000 customers were not satisfied at all?

Answers

Answer:

a. 92%

b. 4425

Step-by-step explanation:

So there are 5000 customers in total, and 100 were completely satisfied, and 15 were satisfied and 10 weren't satisfied a bit. so 100+15 is 115 so 115 people in total were satisfied out of 125 because there were 125, and 115+10 is 125 anyways. So 115/125 is .92, and you can convert that into a percentage, 92% of the 250 customers were satisfied so then 250*5 is 5000, so then just multiply 115 by 5 as well. You get 575. So 575 were satisfied out of the 5000 customers and 5000-575 are the people not satisfied, so 4425.

probably wrong because it doesnt sound right but just try it


Dana bought 12 pizzas for a Math Club party. Some were pepperoni pizzas that $11.00 each,
and the rest were mushroom pizzas that cost $9.50 each. She paid $124.50 for the pizzas. How
many pepperoni pizzas did she buy

Answers

Answer:

7 pepperoni pizzas

Step-by-step explanation:

First, you take the biggest number and subtract it by 9.5 until you get a number that can be divided into 11 which is 77.

Answer:

7 pepperoni pizzas

Step-by-step explanation:

Where p = # of pepperoni pizzas and m = # of mushroom pizzas

124.50 = 11p + 9.5m

Now you need to guess and check:

Use this equation: (124.5 - 11 * p) / 9.5 and replace p with whole numbers until you get a whole number as the output

I got p=7 and m=5

So she bought 7 pepperoni pizzas

if kokichi was in aot would he roast the heck out of the titans and burn them to death?

Answers

Answer: yes

Step-by-step explanation:

Answer: Hell yeah he would

Short King ✋

Help what do I put for 3??

Answers

Answer:

c = 48m

Step-by-step explanation:

For every box, she can make 240/5 = 48 cupcakes. So, the equation is

c = 48m

203/4108 as a percent
a. 4.94%
b. 20.24%
c. 0.049%
d. 49.42%

Answers

4.94% is the correct one.

PLZ HELP WILL GIVE BRAINLIST IF CORRECT!!! IGNORE THE METHODS

Answers

1) 25%of50=$12.5. 50-12.5=37.5

2)20%of21=$4.2. 21-4.2=16.8

3)5%of12=$0.6.    12-0.6=11.4

HOPE THIS HELPED!!!

Answer:

1. $37.50

2.$16.80

3. 0.41

Step-by-step explanation:

Find the slope of the line.

Answers

Step-by-step explanation:

y2-y1/

x2-x1

3-(-3)/

1--2

6/3=2

find the perimeter of the rectangle below

Answers

Answer:

I don't know that but the W is x+1/2

Step-by-step explanation:

hope this helps

Write a sentence to answer each question:

How much warmer is 82 than 40?

Answers

Answer:

82 is 42 degrees warmer than 40

Step-by-step explanation:

if you subtract 40 from 82, you get 42 meaning that the answer will be 42 degrees more than 40

Solve:
V5x+1+6=4
V=square root

Answers

Answer:

the answer is c hope it help

Answer: D

Step-by-step explanation:

1. movethe constanat to the right

2. Calculate

3.The statement is false

Simplify: 70x/2x.
A. 32
B. 33
C. 34
D. 35

Answers

The answer is D. 35. The x’s cancel out because x divided by x is 1 leaving you with 70/2 which is then 35.
Hope this helped.

How many solutions are there to the system of equations shown?

{16x−12y=40
4x−3y=10

I don't really understand these so an explanation would be nice :)

Answers

Step-by-step explanation:

-6 i think

Answer:

infinitely many solutions

Step-by-step explanation:

right on edg

HELP PLEASE 24 POINTS

Answers

Answer:

Option D) the same line.

Step-by-step explanation:

That's your answer. Have a good night.

the answer should be d

Calculate the length of the unknown side of each triangle.
a)
3 cm
5 cm
Give your answers to the nearest mm.

Answers

Answer:

5.8cm or 58mm

Step-by-step explanation:

A mailbox is 2.5 feet tall and casts a 5 foot shadow. Summer is 5 feet tall and is standing next to the mailbox. How long is Summer's shadow?

Answers

Answer:

10 feet

Step-by-step explanation:

2.5/5=5/Summer's shadow

Summer's shadow=25/2.5

Summer's shadow=10 feet

Yo can someone help me

Answers

Answer:

Graph #2

Step-by-step explanation:

I would use Desmos for this, makes it easier to find out which graph is for the equation.

PLS help ASAP I DONT have time to answer this, it also detects if it’s right or wrong.

Answers

Answer:

31.4

Step-by-step explanation:

find the value of given expression

[tex] \sqrt{29 - 4} [/tex]

Answers

So 29-4 =25... which is a perfect square

Answer= +/- 5

Answer:

5

Step-by-step explanation:

[tex] \sqrt{29 - 4} \\ = \sqrt{25} \\ = 5[/tex]

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