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

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.

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:

brainly.com/question/11850611

#SPJ2

find the perimeter of the shaded figure.

Tanner is preparing dinner plates. He has 36 pieces of chicken and 16 rolls. If he wants to make all the plates identical
without any food left over, what is the greatest number of plates Tanner can prepare?

The diagram shows a door that has a window in it. The front faces of the door and the window are similar rectangles that have the dimensions shown.


What is h, the height of the window in centimeters?

8(2 + t) - 5(t - 1)

do you guys know the answer i need help you guy

Please help me thank you

can somebody please help me

What is the slope of (-2,5) (3, -5)
A. -1/2
B. -2
C. 2
D. 1/2

Sue bought five sweatshirts all for the same price. The tax on the purchase was $2.50 and the total was $47.50. What was the cost of each sweatshirt?
Clara lends half her marker collection to her sister, Susan. Clara then buys four more markers. If she has 12 markers now, how many markers did Clara have initially?
show your work
HELP THANKYOUUUUU

amber must make up a vocabulary quiz. she can take it during her lunch or after school on wednesday, thursday, or friday. The tree diagram shows the possible combination of the times she can make up the quiz

Please help me it’s due in a couple of minutes!!!!!!!!

Pennies made after 1984 weigh 2.5 grams. How much would 10 pennies weigh?

A=16.7
B=17
C=23
D=7

Classify the polynomial by degree and number of terms.
2+3x^3-7x^3+10

What is the sum of -7 1/6 + 3 5/6 in simplest form?

►Solve the problems.
I
The tile floor in a restaurant is being replaced. The dimensions of the floor are
shown. What is the total area of the new tile floor in the restaurant?
12 ft
17 ft
15 ft
20 ft
A 64 ft2
B 180 ft2
C 240 ft2
D 300 ft

What is the slope of this line?



Enter your answer as a whole number or a fraction in simplest form in the box.

What triangle is this ????Pleaseeee helppp !!!!!!!!!! Will mark Brianliest correct answer !!!!!!!!!!!!!!

Samantha was training to play basketball. She threw the ball 19 times. Gabrielle wrote down all Samantha's throws and for all the ones who got in the basket she added 5 points. For all the throws that weren't successful, she got rid of 3 points. At the end Samantha got 55 points. How many times did Samantha throw the ball in the basket successfully?

Peter says, "If you subtract 19 from my number and multiply the difference by - 7, the result is
- 140." What is Peter's number?
Peter's number is

II. Mr. Roy sold a cupboard to Mohan for RO 60 and earned a profit of RO 10. Mohan spent RO 27 to polish and repair the cupboard. He then sold it to Gopi at a profit of RO 8. After using the cupboard for a year , Gopi sold it to a furniture dealer for RO 90. Did Gopi make a profit or a loss in the deal? *

Rob was driving his car slowly and then increased its speed by 40.5 miles per hour to reach a top speed of 60 miles per hour. What was his car's initial speed?​

Ten(10) adults and 3 children attend a local concert for $59. Four(4) adults and 3
children attend the same concert for $29. How much does it cost for each to attend?

PLEASE help ASAP will give brainlist

what is the MAD of 82, 72, 45, 91, 58, 83, 65, 87, 90, 77, 73, 89 ?
I'm very confused.

Ashley is a software saleswoman. Her base salary is $1,500, and she makes an additional $60 for every copy pf history is fun she sells. Let P represent her total pay (in dollars), and let N represent the number of copies of History is Fun she sells. Write an equation relating P to N. Then use this equation to find her total pay if she sells 23 copies of History is Fun

What is the fraction that is halfway between 1/3 and 1 1/2

Derek wants to ship items that weigh a total of 7 pounds, and Keisha wants to ship items that weigh a total of 10 pounds. How much more does Keisha pay for shipping than Derek? $4.50 $6.00 $9.50 $12.00

Caroline, Colin & Sarah share some money. Caroline gets 1 /9 of the money. Colin and Sarah share the rest in the ratio 1:3. What proportion does Colin get?

I need this ASAP. Will award brainliest answer.
Thanks

One less than 6 times a number is the same as the number plus 14.
find the equation
x=

Mr. Smith is 81 years older than his grandson, Victor. In 3 years, Mr. Smith will be four times as old as Victor. How old is Victor now?

A) 21 years old

B) 22 years old

C) 24 years old

D) 27 years old