Use synthetic division to find the quotient if polynomial P(x) = x3 – 7x + 6 is divided by x – 2.
Question 17 options:
A)
x2 – 2x + 3
B)
x2 – 2x – 3
C)
x2 + 2x – 3
D)
x2 + 2x + 3
Answers
Answer:
C.) [tex]x^2+2x-3[/tex]
Step-by-step explanation:
They give us the function; [tex]P(x)=x^3-7x+6[/tex], which is then divided by the binomial, [tex](x-2)[/tex].
We can use polynomial synthetic division to solve this! First, let's understand how we must use it properly.
As we can tell from the function [tex]P(x)=x^3-7x+6[/tex] , there is an exponent value of 3, and an "invisible" exponent of one on -7x. When doing the synthetic division, we must put in a zero before we introduce the term '-7x' in our process of division.
The binomial [tex](x-2)[/tex] tells us that we are dividing the function by that, but we have to take the opposite value of the integer value, and here's why.
[tex](x-2)=0[/tex]
If we are trying to solve for 'x' here, we have to add plus sides by two, and we get x=2. That is what we have to put on the left side of the synthetic division we will use, we are essentially stating that one of the root/solution(s) to the function is 2, and we get verification of that when the synthetic division results in zero towards the end.
Then when the synthetic division has been done, since we are dividing by that binomial, we take out the values that we know already, which are '1', '2', and '-3', and take away one power of exponent to each of them (if applicable)
Thus, leaving us with our answer, [tex]x^2+2x-3[/tex].
The required quetient of the given expression is x² - 2x -3. Options C is correct.
What is synthetic division?It is a method for performing division of polynomials, with little writing and lesser calculations than complex division.
here,
synthetic division is given as,
put divisor equal zero,
x - 2 = 0 so x = 2
Now,
Arranging the division with zero and coefficients and constant of the expressions,
2 | 1 0 -7 6
+ 2 4 -6
----------------------------
1 2 -3 0
So, the question, by synthetic division is given as x² + 2x -3.
Thus, the required quetient of the given expression is x² - 2x -3. Options C is correct.
Learn more about synthetic divisions here:
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Related Questions
PLEASE HELP! BRAINLIEST IF CORRECT!
Over a 20-year period, a certain city recorded a total rainfall of 621 inches. The rainfall during this past year was 28 inches. If the variable "r" stands for the total amount of rain for the other 19 years, which of the following units could apply to that variable?
A. months
B. inches
C. years
Answers
Answer: B inches
Step-by-step explanation:
I took the quiz
Answer:
its B
Step-by-step explanation:
can someone help me with this?
Answers
Answer:
A'(-2,0) B'(-3,5) C'(0,4)
Step-by-step explanation:
all u have to do is count each original point 3 units left and 4 units up like what the rule for the translation says.
Answer:
A. (-2,0)
B. (-3,5)
C. (0,4)
Aubree drives 15 miles in 20 minutes. If she drove three hours in total at the same rate, how far did she go
Answers
Tyler went to the super market to buy food for a pantry. He has $36, and can carry up to 20pounds of food in his backpack. One package of pasta is the right amount to go with one jar of pasta sauce. What is the best number of packages of pasta and jar of pasta sauce to buy for the food pantry
Answers
This question is incomplete
Complete Question
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar. Let x = the number of packages of pasta and y = the number of jars of pasta sauce. One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry? Explain your reasoning.
Answer:
Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.
Step-by-step explanation:
Let
x = the number of packages of pasta
y = the number of jars of pasta sauce.
He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
x + 1.5y ≤ 20....... Equation 1
x = 20 - 1.5y
x × $1 + y × $3 = $36
x + 3y ≤ 36..... Equation 2
20 - 1.5y + 3y = 36
-1.5y + 3y = 36 - 20
1.5y = 16
y = 16/1.5
y = 8
And x = 8
Therefore,
Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.
If you have a bit of honesty and sincerity, kindly avoid spamming just for points!
A production process consists of consumption of the following material in Kgs:
49, 50, 38, 60, 75 of materials A, B, C, D. E respectively. How many angle difference between C & D in the pie chart?
a. 25.12% b. 29.12% C.38.15
Need solution with some explanation
Answers
Answer:
29.12%
Step-by-step explanation:
Given that :
A = 49
B = 50
C = 38
D = 60
E = 75
Total = (49 + 50 + 38 + 60 + 75) = 272
Pie chart % for each :
A = (49 / 272) * 360 = 64.85
B = (50 / 272) * 360 = 66.18
C = (38 / 272) * 360 = 50.29
D = (60 / 272) * 360 = 79.41
E = (75 / 272) * 360 = 99.26
Difference between C and D
(79.41 - 50.29) = 29.12%
A man buys a TV. The total cost is $2,500, and the sales commission is 8%. How much should the salesperson get as commission for this sale?
Also please show me how you got the answer cause i have to show my work!!!
Answers
Answer:
$200
Step-by-step explanation:
First Change the percent to a decimal
In this case the percent was %8, change it into a decimal; 8%=.08
Next multiply 2,500 x .08 which gives you 200
The answer is $200! Hope this helps!.
What is 9 to the first power times (-2)3?
(A) -27
(B) 36
(C) -72
(D) 27
Answers
Answer:
-72
Step-by-step explanation:
9*(-2)³ = 9*(-8) = -72
Answer:
(C) -72
Step-by-step explanation:
[tex]9^1*(-2)^3[/tex]
Any number to the exponent of 1 is equal to themselves
[tex]= 9*(-2)^3[/tex]
Solve the exponent and multiply
[tex]= 9*(-8)\\=-72[/tex]
I hope this helps!
Hi does anyone know the answer to these two math questions? ( order of operations )
Answers
Answer: here's the answers to the problems
6) 17
8) 2.5
Answer:
6. 17
8. 2.5
Step-by-step Explanation:
4 x 3 + 6+9/3 12/3 + 2+7/5-3 - 6
12 + 15/3 4 + 9/2 - 6
12 + 5 4 + 4.5 - 6
= 17 8.5 - 6
= 2.5
I just need one and two
Answers
Answer:
b. is not a function
and for question 2 the answer is a.
Step-by-step explanation:
1. B is the answer because one of the inputs has more than one output
2. When you solve it and connect the dots it forms that kind of curve.
Sandra drove 90 miles and used 6 gallons of gasoline. Ben drove 135 miles and used 9 gallons of
gasoline
Which of these statements is true?
A Sandra and Ben used gasoline at the same rate because - 15
B Sandra and Ben used gasoline at different rates because Ben drove a longer distance.
C Sandra and Ben used gasoline at the same rate of 12 miles per gallon.
Sandra and Ben used gasoline at different rates because Sandra used less gasoline.
Answers
Answer:
It is A
Step-by-step explanation:
6 x 15 = 90
9 x 15 = 135
Answer: A
Step-by-step explanation:
because the rate Sandra is using gas is 90/6 which is 15 and the rate Ben is using gas is 135/9 which is also 15. Since they are USING the gas, it is minus 15 (-15).
estimate 193.87 ÷ 5
Answers
Answer:
38.774
Step-by-step explanation:
Answer:38.774
Step-by-step explanation:
why is b the answer ???????????????????/
Answers
Answer:
Step-by-step explanation:
its b cuz when u replace any value of x from B to the equation, the value of y satisfies the values of y in B. For instance
y = 4 * -3 + 2
= -10
the value of y is -10 which satisfies the value of y in B but when u use a value of another table suppose A it would be,
y = 4 * 7 + 2
= 30
but the value y corresponding to the value of x we used is not 30
HOPE IT HELPED
Sangeet got 96% of his answers right in a test of 50 marks. What was his score out of 50?
Answers
Answer:
48/50
Step-by-step explanation:
So find 96 percent of 50
Now divide it
48/50
You dont gotta divide, leave it as fraction
What is being done to the variable in the equation m/5 = -40?
A. It's being multiplied by -40.
B. It's being multiplied by -5.
C. It's being divided by -40.
D. It's being divided by 5.
Answers
Answer:
d. its being divided by 5
brainliest if correct1+1
Answers
Answer:
11
Step-by-step explanation:
:>
Answer:
1+1=2 is the answer
Step-by-step explanation:
mark me as brainlist
If the lengths of two sides of a triangle are 10 meters and 14 meters, which of the following measures is the
possible length of the third side?
O 2 meters
O 4 meters
O 22 meters
O 24 meters
Answers
The rule is that the two smallest sides need to add up to be greater than the largest side.
2 meters + 10 meters is smaller than 14, so it doesn’t work
4 meters + 10 meters is only equal to 14, so it doesn’t work either
10 meters + 14 meters IS greater than 22, so it does work
10 meters + 14 meters is equal to 24, so it doesn’t work.
Explanation: You need a bigger side if you have two smaller sides.
Helpppppp please......................................
Answers
I hope this helps, have a good day
Step-by-step explanation:
4. - 5a>1-3
5a<2
a<2/5
5. - 2b<-6-27
2b>33
b>33/2
6. 1/2(c+1)>5
c+1>10
c>9
7. A. The club earns 10*p $
B. Difference 10*p - 75
C.
[tex]p \geqslant \frac{(75 + 50)}{10} [/tex]
[tex]p \geqslant \frac{125}{10} [/tex]
Danny charges $44 for 4 hours of swimming lessons, Martin charges $42 for 3 hours of swimming lessons. Who offers a better deal?
Answers
Answer:
I would say that Danny's deal is better.
Step-by-step explanation
If you wan t to know the better deal you should first figure out how much they charge per hour. All you have to do is divide the price by the amount of hours.
Danny: 44 ÷ 4 = 11
Martin: 42 ÷ 3 = 14
Martin charges more money for fewer hours. Danny charges less for 4 whole hours, so he would be the better deal!!!
Here is a list of numbers:
20, 8, 6, 11, 3, 15, 11 ,20 ,12 ,13
State the median.
Answers
Answer: 18
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
1. Arrange the numbers from least to greatest.
3,6,8,11,11, 12,13,15, 20
2. Start from the two ends and cross them off until you're left with what's in the middle.
6,8,11,11,12,13,15
8,11,11,12,13
11,11,12
11
3. The median is 11 because that is the number you are left with.
A small town has two local high schools. High School A currently has 500 students and is projected to grow by 80 students each year. High School B currently has 700 students and is projected to grow by 30 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine how many students would be in each high school in the year they are projected to have the same number of students.
Answers
The equation that represent the number of students in High School A at time t is AA = 500 + 80tt.
The equation that represent the number of students in High School B at time t is BB = 700 + 30tt.
The number of students when both schools would have the same number of students is 820.
When would the school have the same number of students?
The equation that represent the number of students in High School A :
current number of students + (number of years x rate of increase)
AA = 500 + 80tt.
The equation that represent the number of students in High School B at time t is:
current number of students + (number of years x rate of increase)
BB = 700 + 30tt.
When the schools would have the same number of students, the two equations would be equal:
700 + 30tt = 500 + 80tt
700 - 500 = 80tt - 30tt
200 = 50tt
tt = 200 / 50
tt = 4
Population = 500 + (80 x 4)
500 + 320 = 820
To learn more about linear equations, please check: https://brainly.com/question/26434260
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What is 5=-2/3x+b X=4
I’ll give Brainlylist
Answers
Answer:
b = 23/3
Step-by-step explanation:
5 = -2/3(4) + b
5 = -8/3 + b
5 + 8/3 = b
b = 23/3
2. (05.04)
18x - 6
Simplify_9x
(2 points)
1
15x + 5
21x²
Please help!!
Answers
Answer:
i cant cus i am only the age of thirteen
Need help asap!! plss
Answers
For the second i think it’s irrational bcsz S would not be expressed as an integer
18 cajas de manzanas y peras fueron llevadas a la escuela. Las peras trajeron 210 kg en 6 cajas. ¿Cuántos kilos de manzanas fueron llevadas a la escuela si cada caja de manzanas pesa 7 kg más que una caja de peras 18 cajas de manzanas y peras fueron llevadas a la escuela. Las peras trajeron 210 kg en 6 cajas. ¿Cuántos kilos de manzanas fueron llevadas a la escuela si cada caja de manzanas pesa 7 kg más que una caja de peras?
Answers
Answer:
504 kilos de manzanas fueron llevados a la escuela.
Step-by-step explanation:
Sean [tex]x[/tex], [tex]y[/tex] la cantidad de cajas de manzanas y peras, respectivamente. De acuerdo con el enunciado, tenemos el siguiente sistema de ecuaciones:
Total de cajas
[tex]x+y = 18[/tex] (1)
Masa de cada caja de peras
[tex]y\cdot m_{P} = 210[/tex] (2)
[tex]y = 6[/tex] (3)
Masa de caja de manzanas
[tex]m_{M} = m_{P}+7[/tex] (4)
De (2) en (3), tenemos que la masa de cada caja de peras es:
[tex]m_{P} = 35\,kg[/tex]
Por (4), encontramos que la masa de cada caja de manzanas es:
[tex]m_{M} = 35\,kg+7\,kg[/tex]
[tex]m_{M} = 42\,kg[/tex]
Finalmente, de (1) tenemos la cantidad de cajas de manzana:
[tex]x = 18-y[/tex]
[tex]x = 12[/tex]
La cantidad de kilos de manzanas llevada a la escuela se obtiene al multiplicar la cantidad de cajas de manzana por la masa de cada caja:
[tex]M = (12)\cdot (42\,kg)[/tex]
[tex]M = 504\,kg[/tex]
504 kilos de manzanas fueron llevados a la escuela.
HELP ME PLEASE
Mr. Parke made snacks in separate gift bags. He gave one each to the 86 seventh grade students going on the field trip. Then he gave 17 bags to the students in Mrs. Mark's class for decorating the trophy cases. Next he gave 11 to the students in Mrs. Green's class for helping during the school play. Mr. Parke had 11 snacks left. How many snacks did he make?
Answers
Answer:
125 snacks
Step-by-step explanation:
just add every number
Answer:
125
Step-by-step explanation:
if I would have 160$ and was discounted by 75 percent and if used a PROMO CODE and it gave me 10 percent off how much would I have
Answers
Answer:
10 percant off how much would i have
Find the probability that when a hand of 7 cards are drawn from the well-shuffled deck of 52 cards, it contains
(i) all kings (ii) 3 kings
Answers
Answer:
(i) 0/7
(ii) 3/7
Step-by-step explanation:
In a deck of 52 playing cards, there are 13 cards of each clubs, spades, diamonds, and hearts. From those 13 cards, each group has 1 King, Queen, Jack respectively.
No.of total outcomes = 7
(i) In the entire 52 cards, there will be 4 Kings.
The probability of getting 4 kings in 7 cards can be 4/7.
But since there are only 4 kings (4<7), the probability of getting all kings in 7 cards would be 0/7.
There are 10 members on the school Hungry Hungry Hippos club. They meet Thursdays to play Pokemon. Each member wants to play four games against each of the other members. How many games will be played in total?
Answers
Answer:
40 games will be played in total.
Step-by-step explanation:
NEED HELP ASAP, WILL GIVE BRAINLIEST TO CORRECT ANSWER
According to the Fundamental Theorem of Algebra, the graph of f(x) = -x 2 - 2x + 1, has ______ rational roots.
A) One
B) Two
C) Three
Answers
If plugging to the standard formula, you will only have one answer. Thus one rational root
Eddie compared prices of two auto-rental agencies for the use of a mid-size auto for one week. Right Price Auto charged a flat fee of $386 plus 20¢ per mile driven. EconoCar charged a flat fee of $344 plus 35¢ per mile driven. Which equation should he use to determine the distance in miles, m, that would make the total charges of both auto-rental agencies equal?
Answers
Answer:
What are the options?
Step-by-step explanation:
Answer: I would help you but I do no know the answer to this either and I will help you later have a nice day
Step-by-step explanation: