How is factor theorem derived?

Answers

Answer 1

Factor theorem is most commonly used for factoring a polynomial or integer and searching the roots of the polynomial. It is a particular case of a polynomial remainder theorem.

As defined in the introduction, a polynomial f(x) has a factor (x-a), if and only if, f(a) = 0. It is one of the processes to do the factorization of a polynomial.

Here we can prove the factor theorem, according to which we can.

factories the polynomial.

Consider a polynomial f(x) which is divided by (x-b), then f(c)=0.

Using remainder theorem,

f(x)= (x-b) q(x)+f(b)

Where f(x) is the target polynomial and q(x) are the quotient polynomial.

because f(b) = 0, So,

f(x)= (x-b) q(x)+f(b)

f(x) = (x-b) q(x)+0

f(x) = (x-b) q(x)

So, (x-b) is a factor of the polynomial f(x).

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Related Questions

Debra made $228 for 12 hours of work.
At the same rate, how many hours would she have to work to make $323?

Answers

Answer:

17 hours

Step-by-step explanation:

Set up a proportion: [tex]\frac{12}{228} = \frac{x}{323}[/tex]  Cross multiply, then divide: 12 × 323 = 3876, 3876 ÷ 228 = 17So, she would have to work 17 hours to make $323.

I hope this helps!

Which expression is equivalent to 1/2b -15?

A. -1/2 (b + 30)

B. -1/2 (b - 30)

C. 1/2 (b - 30)

D. 1/2 (b + 30)

Answers

C

Using the distributive property, 1/2(b - 30) would end up being (1/2b) - ((1/2)30). 1/2 times 30 is 15. So 1/2b - 15.

The  expression  1/2b -15 is equivalent to, 1/2(b-30), So option C is correct

What are expressions?

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

An expression,  1/2b -15

The expressions are equivalent = ?

So now, we can take 1/2 common from the expressions

⇒    1/2b -15(2/2)

⇒   1/2(b -15×2)

⇒   1/2(b - 30)  

Hence, the equivalent expression is,  1/2(b - 30)  

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Evaluate the expression for p = 9!

Answers

Answer:

362880

Step-by-step explanation:

P=3.14 and 3.14 times 9 equals 28.26

ILL GIVE BRAINLIEST FOR FIRST ANSWER HELP


What is the volume of this rectangular prism?

Answers

Answer:

The answer is 56 cm^3

Step-by-step explanation:

2 = height

7 = length

4 = width

Formula: LxWxH

2 x 7  x 4 = 56

Jan wants a bunch of balloons for her birthday party. There were 10 red, 12 blue, 13 green and 15 yellow balloons. What percentage is the blue balloons ?

Answers

Answer:

Should be 24%

Step-by-step explanation:

12/50= .24

2.

Which equation best describes the graph??

y = 3x + 1
y = -3x + 1
y = -3x - 1
y = 3x - 1

Answers

Answer:

y = 3x + 1

Step-by-step explanation:

Use the Distributive Property to find the product.

1 1/5x25=?

The product is .

Answers

Answer:

55

Step-by-step explanation:

you make 25 into its perfect square form and multiply

11÷5 x 5 x 5

Diane looked out the window in the store parking lot and said, “There are 13 motorcycles and cars in the lot.” Steve looked out the window and said, “I see 42 wheels.”

Question: How many motorcycles and how many cars are in the parking lot?

Answers

Answer:

There are 5 motorcycles and 8 cars in the parking lot.

Step-by-step explanation:

Set variables X to represent the number of cars and Y to represent the number of motorcycles. You will get the following equations:

X + Y = 13 (Total number of motorcycles and cars)

4X + 2Y = 42 (Total number of wheels)

Combine the two equations together and solve for Y and X

4(13 - Y) + 2Y = 42 note: X = 13 - Y

52 - 4Y + 2Y = 42

-2Y = -10

Y = 5

X + 5 = 13

X = 8

What is the value of Fraction 1 over 2 x3 + 3.4y when x = 3 and y = 4? (4 points)15.85 18.1 27.1 31.6

Answers

The correct answer is 27.1

the product of 9 and c

Answers

Answer:

The answer is 9c or 9 × c..

Help needed ASAP, please!

Answers

Answer:

percent 60%

fraction 60/100

ratio 60:40

(dk if it is)

Answer: 60% fraction: 6/10 ratio: 6:10

Step-by-step explanation:

Solve for y when f(x)=2x^4-5

Answers

if you are looking for the y intercept it is (0,-5) or -5

Find the 9th term of the geometric sequence 6, -24, 96,

Answers

Step-by-step explanation:

the process is show in the above picture.

What is the slope between:
(2,5) (4, 13)

Answers

Answer:

m = 4

you can find the answer for this on m a t h w a y (without the spaces)

I hope this helps!

Answer:

4

Step-by-step explanation:

slope = y2-y1 / x2-x1

13-5= 8

4-2=2

8/2= 4

Determine if it’s relationship is a function.

Answers

Answer:

It is not a function

because: 4: 25 went to 4: 35

an input can not have two or more outputs

Step-by-step explanation:

A blueprint for a new triangular playground shows that the sides
measure 480 ft, 140 ft, and 500 ft. Is the playground in the shape of
a right triangle? Explain.

Answers

Answer:

no

Step-by-step explanation:

because it is not equal numbers

Just look at the picture please fast I WILL MAKE BRAINLIEST!!!!!!!!

Answers

Answer:

A (-3,0) B (0,-1) C (1,-4)

Step-by-step explanation:


can someone solve this please , ill give Brainly to whoever is first :)

Answers

Answer:

630 in^2

Step-by-step explanation:

21 x 15 divided by 2 = 157.5

157.5 x 4 = 630

Answer:

Step-by-step explanation:

I person who answers this is right

The measures of the angles of a triangle are shown in the figure below.Solve for X

Answers

x=9, all angles will add up to 180. 180-63-38=79. 79=9x-2. 81=9x. divide by 9, x=9.

please help w steps! asap

Answers

Answer:

(4,6)

Step-by-step explanation:

The midpoint=([tex]\frac{5+3}{2} ,\frac{11+1}{2} )[/tex]

                      =(4,6)

14 =2b HELP ME PLEASE

Answers

Answer:

The answer is b = 7

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

~Hoped this helped~

Divide 2b by 2 to get b. Then divide 14 by 2 to get 7. b=7

Solve for the volume of the 3D shape.

27 m3

27

180 m3

180m

360 m3


360 m

Answers

Answer:

360 m3

Step-by-step explanation: just multiply 18m times 5m times 4 m then you get your answer :)

hope this helps :D

Answer:

360 m3

Step-by-step explanation:

Make the other guy brainlist cuz he helped me. :p

A seventh-grade student wants to read at least 300 pages of a novel this week. He has already read 55 pages. An inequality that represents this situation is 7x+55≥300.

Solve this inequality for x, the number of pager per day.
Identify a number of pages that the student could read per day in order to have at least 300 pages of the novel read in a week.
Explain how you know that your answer is appropriate.
Enter your answer and your work or explanation in the space provided.

Answers

Answer:

x=35

Step-by-step explanation:

7x+55≥300

    -55 -55

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

7x≥245

now divide both sides by 7

x=35

4. What is the axis of symmetry for h(x) = 19(x – 5)^2 + 6

Answers

Answer:

x = 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

(h, k ) are the coordinates of the vertex and a is a multiplier

h(x) = 19(x - 5)² + 6 ← is in vertex form

with vertex (h, k ) = (5, 6 )

The axis of symmetry is a vertical line passing through the vertex

with equation x = 5

Part A: If PM =PN and MPQ=UNPQ which triangle congruency postulate can we
use to determine APMQ = APNQ given the information on the figure?
OSAS
O SSS
O AAS
O ASA
Part b:How did you determine your answer in part A/Question 2?

Answers

Answer:the answer for part A is SAS.

Step-by-step explanation:

We already know that side PQ is the same length for both the triangles. We were then given the information that sides PM and PN were equal. So now we already have two sides that are the same. Then we were given the information that angle MPQ and angle NPQ were also equal. So now we have two sides and an angle that are equal. This is how we got SAS (side angle side). I tried my best to explain. I added a photo so you could see what I was trying to explain. Hopefully this helped!

Will Mark brainliest if answer both correctly / What is X= ? / conditional statement

Answers

The answer is for 1st question is “10.4” and for the second question “non of these choices are correct”.

Explanation:

For the 1st question:

tan = opposite / adjacent

tan 30 = x / 18

18 tan 30 = x

x = 10.4

For the 2nd question,
If a triangle as an angle of 90 degree, it is 100% a right triangle.

Hope it helps :), mark me brainliest please!

Write two expressions which are equivalent to 24x + 8.

Answers

[tex]8(3x + 1)[/tex]

Factor out 8 from the expression

Subtract 1/2h - 1 from 3/4h + 4

A: -1/4h
B: 1/4h + 3
C: -1/4h + 5
D: 1/4h + 5

Answers

Answer:

option d.......................

solve this system of equations by using the elimination method.

2x-3y=25
5x+3y=10

Answers

Elimination method is my favorite way to solve 2 equations like this written in standard form! First I'm going to rewrite the equations and mark numbers to make this explanation more clear.

2x-3y=251️⃣

5x+3y=102️⃣

Looking at these 2 equations we can see that there is a +3 and a -3. This could be eliminated by adding the 2 equations together! *Remember what is on the left side adds with the left side, and what's on the right side adds with the right side. Therefore we can do:

1️⃣+2️⃣

2x-3y+5x+3y=25+10

7x=35

x=5

Then we can substitute the value of x back into either of the 2 equations.

2*5-3y=25

10-3y=25

3y=-15

y=-5

Then write the 2 answers together.

{x=5

{

{y=-5

Now we can check our answers.

2*5-3*-5=10- -15= 10+15=25 Correct

5*5+3*-5= 25+ -15= 10 Correct

From this we can see that x=5 y=  - 5 are the correct answers!

Laila and Young each made a model volcano. Laila's volcano weighs 3 times as much as Young's. Laila's volcano weighs 9 pounds.
How much does Young's volcano weigh?
A3 pounds
B. 6 pounds
c 12 pounds
D. 18 pounds
E 27 pounds

Answers

Answer:

3

Step-by-step explanation:

The answer to this question is A
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