SOLUTION: What is the remainder when {{{x^7-x^6+x^5-x^4+4}}} is divided by {{{x-1}}}

Algebra.Com
Question 149767: What is the remainder when is divided by
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Let's simplify this expression using synthetic division


Start with the given expression

First lets find our test zero:

Set the denominator equal to zero

Solve for x.

so our test zero is 1


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 , , and . This is simply because really looks like
1|1-11-10004
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
1|1-11-10004
|
1

Multiply 1 by 1 and place the product (which is 1) right underneath the second coefficient (which is -1)
1|1-11-10004
|1
1

Add 1 and -1 to get 0. Place the sum right underneath 1.
1|1-11-10004
|1
10

Multiply 1 by 0 and place the product (which is 0) right underneath the third coefficient (which is 1)
1|1-11-10004
|10
10

Add 0 and 1 to get 1. Place the sum right underneath 0.
1|1-11-10004
|10
101

Multiply 1 by 1 and place the product (which is 1) right underneath the fourth coefficient (which is -1)
1|1-11-10004
|101
101

Add 1 and -1 to get 0. Place the sum right underneath 1.
1|1-11-10004
|101
1010

Multiply 1 by 0 and place the product (which is 0) right underneath the fifth coefficient (which is 0)
1|1-11-10004
|1010
1010

Add 0 and 0 to get 0. Place the sum right underneath 0.
1|1-11-10004
|1010
10100

Multiply 1 by 0 and place the product (which is 0) right underneath the sixth coefficient (which is 0)
1|1-11-10004
|10100
10100

Add 0 and 0 to get 0. Place the sum right underneath 0.
1|1-11-10004
|10100
101000

Multiply 1 by 0 and place the product (which is 0) right underneath the seventh coefficient (which is 0)
1|1-11-10004
|101000
101000

Add 0 and 0 to get 0. Place the sum right underneath 0.
1|1-11-10004
|101000
1010000

Multiply 1 by 0 and place the product (which is 0) right underneath the eighth coefficient (which is 4)
1|1-11-10004
|1010000
1010000

Add 0 and 4 to get 4. Place the sum right underneath 0.
1|1-11-10004
|1010000
10100004



Since the last column adds to 4, we have a remainder of 4.


--------------------------------------------

Answer:

So when is divided by , the remainder is 4
RELATED QUESTIONS

Hello can someone help with this problem? What is the remainder when x^7-x^6+x^5-x^4+4 (answered by stanbon)
When x is divided by 7, the remainder is 5. What is the remainder when 5x is divided by... (answered by ikleyn)
What is the remainder when 6x^4-3x^5+2x^3+x-3 is divided by x+1? Thank... (answered by ReadingBoosters)
What is the remainder when f(x)=-8x^25+x^11-x^4+9x is divided by x-1? (answered by ikleyn)
what is the remainder when P(x)=x^(2)+5 is divided by (x+1) (answered by Theo,ikleyn)
Find the quotient and remainder when P(x)=x^4+x^3+2x is divided by... (answered by Boreal,stanbon)
when the polynomial p(x) is divided by (x-2) the remainder is 4 and when p(x) is divided... (answered by JThomson)
Use the remainder theorem to find the remainder when f(x) is divided by g(x)... (answered by ramkikk66)