1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
krok68 [10]
2 years ago
8

Use synthetic division to solve (x3 + 1) ÷ (x – 1). What is the quotient?

Mathematics
2 answers:
kolbaska11 [484]2 years ago
6 0

The quotient is of the division of {x^3} + 1 and x - 1 \:is \:\boxed{{x^2} + x + 1} and the remainder is \boxed2.

Further explanation:

The numerator of the division is {x^3} + 1 and the denominator isx - 1.

Solve the given polynomial P\left( x \right) = {x^3} + 1 to obtain the quotient by the use of synthetic division.

Now obtain the value of x from the denominator.

\begin{aligned} x - 1&= 0 \\x &= 1\\\end{aligned}

Divide the coefficients of the polynomial by  , to check whether   is a zero of the polynomial.

\begin{aligned}1\left| \!{\nderline {\,{1\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,1\,} \,}} \right.\hfill \\\,\,\,\,\underline {\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,1}\hfill \\\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,2 \hfill\\\end{aligned}

The last entry of the synthetic division told about remainder and the last entry of the synthetic division is 2. Therefore, the remainder of the synthetic division is  .

The entry in the last line of synthetic division gives us the coefficients of the quotient.

The new numbers are the coefficients of the quotient.

The quotient is of the division of {x^3} + 1 \:and \:x - 1 \:is\: \boxed{{x^2} + x + 1} and the remainder is \boxed2.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Synthetic Division

Keywords: division, synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.

mamaluj [8]2 years ago
4 0
Steps:

Use the divisor and find x :
x - 1 = 0  **add 1
x= 1
Now we will use the 1 in dividing:

take the coefficients from in front of all terms
   ** make sure you include 0's for x^2 and x since you have to have all terms

set it up with a 1 in a box:

1|  1   0   0  1   **bring the first number down
____________
     1                    **multiply the boxed number by the first number and add it                                 to the second number

1|  1   0   0  1   
____+1_____       **repeat with the rest of the terms
     1   1   

1|  1   0    0    1
  ___+1_+1_+1   
     1   1    1    2                              
**when you're done, use the new numbers to write an equation starting with a term with a degree one less than the previous equation.
**since there is a remainder, rewrite it divided by the original divisor

final answer:
x^2 + x + 1 + (2/ x -1)
You might be interested in
Please help as soon as possible <3
Arte-miy333 [17]

Volume of Cube1

= s³ = 8³ = 512ft³

Volume of Cube2

= s³ = 6.5³ = 274.625ft³

Difference in volume

237.375ft³

7 0
2 years ago
Read 2 more answers
Which is the graph of the equation y-1 =
Alex73 [517]

Answer: 60

Just put 60 :)

7 0
2 years ago
PLEASE SOMEONE HELP ME WITH THIS PROBLEM
AnnZ [28]

Answer:

1.28

2. -3.5

3.-10.5

Step-by-step explanation:

1.-0.0035 · 12000+70= 28

2. -0.0035 ·21000+70=-3.5

3. -0.0035 ·23000+70=-10.5

I hope this helps

7 0
3 years ago
Molly now blends 6 ml of blue paint with 5 ml of white paint. She decides that she likes this color and wants to make more. If s
Stella [2.4K]

9514 1404 393

Answer:

  48 mL

Step-by-step explanation:

The amount of white paint she added is 40/5 = 8 times the amount she already had. So, Molly needs to add 6·8 = 48 ml of blue paint to her mix.

6 0
2 years ago
What is the equation of the line that is perpendicular to f(x) and passes through the point (4, –6)
AnnZ [28]
What is the first equation?

Remember perpendicular lines have reciprocal slopes.

So if we have 1/2 we flip to fraction and sign becoming -2.

You then input the point to find the y-intercept.
3 0
2 years ago
Read 2 more answers
Other questions:
  • Convert this number expressed in standard form to scientific notation. 28,500,000 1. Move the decimal to create the coefficient:
    15·2 answers
  • A father's age is three less than two times the son's age. The difference in their ages is 30 years. Find the son's age.
    15·1 answer
  • Choose Yes or No to tell if the digit in the ones place is 110 the value of the digit in the tens place.
    13·1 answer
  • D. The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shutt
    13·1 answer
  • AHHHHHHhh asap plz answer!!
    7·2 answers
  • Can someone help with this ASAP !
    11·1 answer
  • Terrence and three of his friends are sharing
    5·2 answers
  • Identify the relationship between 8 and 6
    9·2 answers
  • Select the correct answer from each drop-down menu.
    11·1 answer
  • Write 1/4 as an equivalent fraction with denominator 24
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!