[kevinkevin]

  I am working on a challenge problem and the question asks me to divide a polynomial that would be impossible to do using just regular methods.  We are suppose to use another method to solve it.  The the question tells us to do the following division, 6x^1000-17x^562+12x+26 / x+1. I thought that the division algorithm might help,
P(x)= D(x)Q(x)+R(x) but it doesn't because Q(x) and R(x) are unknown.  P(x) is the original polynomial, D(x) is the divisor, Q(x) is the quotient, and R(x) is the remainder.  Then I thought about using the rational zeros theorem, p/q  where p is a factor of the constant coefficient and q is a factor of the of the leading coefficient.  The problem with this is that when we start to get to larger numbers for x the 1000 and 27 power on the x lead to really high numbers.  I need some advice, what should be done to solve this problem.  Thanks           

[curiouscat]

Remainder Theorem
Synthetic Division

[kevinkevin]

  I was thinking about the remainder theorem but I am not quite sure how to execute it.  Don't I have to know what the remainder is in the first place?  And to get the remainder I have to do the synthetic division correct?   Synthetic division should take a long time, right?             

[curiouscat]

   Don't I have to know what the remainder is in the first place?  And to get the remainder I have to do the synthetic division correct?   

No. x= -1 substituted in that poly. will give you the remainder. Simple (if I haven't blundered! )

[kevinnn]

Wow, I feel really stupid.  I over complicate everything. Thanks for the *delete me* 

[curiouscat]

Wow, I feel really stupid.  I over complicate everything. Thanks for the *delete me*

Glad to help.