Mathematics, 30.12.2019 21:31 ctyrector

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

Answers: 2

Show answers

Answers

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
x^2 + x + 1 + (2/ x -1)

Answer from: samone26

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 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://link.

2. Learn more about equation of circle link.

3. Learn more about range and domain of the function link

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.

Answer from: Quest

answer: what are the following choices

Answer from: Quest

If i could just have the statements, i'd be able to

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Will give brainliest what is the value of x? enter your answer in the box.

Answers: 1

Answer

Mathematics, 21.06.2019 17:00

Lisa has three classes that each last 50 minutes. what is the total number of minutes of the three classes

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

Answers: 2

Answer

Mathematics, 21.06.2019 22:20

Which of the following describes how to translate the graph y = |x| to obtain the graph of y = |x+1|+1? shift 1 unit left and 1 unit down shift 1 unit left and 1 unit up shift 1 unit night and 1 unit down shift 1 unit nght and 1 unit up