SOLUTION: Perform divisions 8x^3-6x^2+2x/ 4x+1

Algebra.Com
Question 92270: Perform divisions
8x^3-6x^2+2x/ 4x+1

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 -1/4


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.(note: remember if a polynomial goes from to there is a zero coefficient for . This is simply because really looks like
-1/4|8-620
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 8)
-1/4|8-620
|
8

Multiply -1/4 by 8 and place the product (which is -2) right underneath the second coefficient (which is -6)
-1/4|8-620
|-2
8

Add -2 and -6 to get -8. Place the sum right underneath -2.
-1/4|8-620
|-2
8-8

Multiply -1/4 by -8 and place the product (which is 2) right underneath the third coefficient (which is 2)
-1/4|8-620
|-22
8-8

Add 2 and 2 to get 4. Place the sum right underneath 2.
-1/4|8-620
|-22
8-84

Multiply -1/4 by 4 and place the product (which is -1) right underneath the fourth coefficient (which is 0)
-1/4|8-620
|-22-1
8-84

Add -1 and 0 to get -1. Place the sum right underneath -1.
-1/4|8-620
|-22-1
8-84-1

Since the last column adds to -1, we have a remainder of -1. This means is not a factor of
Now lets look at the bottom row of coefficients:

The first 3 coefficients (8,-8,4) form the quotient



and the last coefficient -1, is the remainder, which is placed over like this





Notice the denominator , the x term has a coefficient of 4, so we need to divide the quotient by 4 like this:


Putting this altogether, we get:



So

which looks like this in remainder form:
remainder -1


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

RELATED QUESTIONS

Perform the indicated divisions. 8x^3 -6x^2 + 2x / 4x +1 (answered by Edwin McCravy)
Perform the indicated divisions:... (answered by lekelly)
Divisions 8x^3 - 6x^2 + 2x/ 4x +... (answered by ankor@dixie-net.com)
Perform the indicated divisions. 8x^3 -6x^2 + 2x / 4x +1 This is what I got is it... (answered by stanbon,Earlsdon)
Perform the indicated divisions. 8x^3 - 6x^2 + 2x ________________ 4x + 1 I... (answered by longjonsilver)
perform the indicated divisions. 8x^3 - 6x^2 + 2x / 4x + 1 I would appreciate a... (answered by ankor@dixie-net.com,jim_thompson5910)
perform the indicated divsions 8x^3-6x^2+2x divided by... (answered by jim_thompson5910)
Divide... (answered by atif.muhammad)
8x^3-6x^2+2x divided by... (answered by 303795)