SOLUTION: The result of dividing x4 - 2x3 + x2 - 3x + 2 by x - 2 is I came up with x3 + x - 1 Is this right?

Algebra.Com
Question 90278: The result of dividing x4 - 2x3 + x2 - 3x + 2 by x - 2 is
I came up with x3 + x - 1
Is this right?
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Start with the given polynomial

First lets find our test zero:

Set the denominator equal to zero
Solve for x.

so our test zero is 2


Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.
2|1-21-32
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
2|1-21-32
|
1

Multiply 2 by 1 and place the product (which is 2) right underneath the second coefficient (which is -2)
2|1-21-32
|2
1

Add 2 and -2 to get 0. Place the sum right underneath 2.
2|1-21-32
|2
10

Multiply 2 by 0 and place the product (which is 0) right underneath the third coefficient (which is 1)
2|1-21-32
|20
10

Add 0 and 1 to get 1. Place the sum right underneath 0.
2|1-21-32
|20
101

Multiply 2 by 1 and place the product (which is 2) right underneath the fourth coefficient (which is -3)
2|1-21-32
|202
101

Add 2 and -3 to get -1. Place the sum right underneath 2.
2|1-21-32
|202
101-1

Multiply 2 by -1 and place the product (which is -2) right underneath the fifth coefficient (which is 2)
2|1-21-32
|202-2
101-1

Add -2 and 2 to get 0. Place the sum right underneath -2.
2|1-21-32
|202-2
101-10

Since the last column adds to zero, we have a remainder of zero. This means is a factor of

Now lets look at the bottom row of coefficients:

The first 4 coefficients (1,0,1,-1) form the quotient




So


So in other words, you are correct.


You can use this online polynomial division calculator to check your work



RELATED QUESTIONS

Find the quotient and remainder of f(x) = x4 -2 divided by p(x) = x-1 Possible... (answered by pradhyumna.kumar@gmail.com)
Find the quotient and remainder of f(x) = x4 -2 divided by p(x) = x-1 Possible... (answered by pradhyumna.kumar@gmail.com)
What is the result of dividing 3x^2+7x^2+5 by x+1 (answered by CubeyThePenguin)
Use the Remainder Theorem to find P(c). P(x) = x4 + 3x2 + 1, c = 3 I came up with 107 (answered by jim_thompson5910)
what is the factorization of 9x^4 - 3x^2? I came up with the answer being..3x^2(x2 -... (answered by richwmiller,Alan3354)
1+ 2/x+ 4/x2+ 8/x3 __________________ 1-... (answered by Fombitz)
. Evaluate 1 + x + x2/2! + x3/3! + x4/4! + ....... (answered by tommyt3rd)
Subscript notation is frequently used for working with larger systems of equations. Use a (answered by ikleyn)