SOLUTION: i need the quotient of -57s^(6)t^(4)-9s^5t^(3)+15s^(4)t^(2)+57s^(2)t and 3s^(2)t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: i need the quotient of -57s^(6)t^(4)-9s^5t^(3)+15s^(4)t^(2)+57s^(2)t and 3s^(2)t      Log On


   

Question 716108: i need the quotient of -57s^(6)t^(4)-9s^5t^(3)+15s^(4)t^(2)+57s^(2)t and
3s^(2)t
Found 2 solutions by mananth, jsmallt9:
Answer by mananth(16946) About Me  (Show Source):
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Fractions represent a division. And the easiest way to solve this is to write is as a fraction and then reduce the fraction:

First we factor out the greatest common factor (GCF) in the numerator and denominator:
%283s%5E2t%28-19s%5E4t%5E3-3s%5E3t%5E2%2B5s%5E2t%2B19%29%29%2F%281%2A3s%5E2t%29
As we can see, we can reduce this fraction. (If we could not reduce the fraction then we would have to resort to long division.)

leaving:
%28-19s%5E4t%5E3-3s%5E3t%5E2%2B5s%5E2t%2B19%29%2F1
which simplifies to:
-19s%5E4t%5E3-3s%5E3t%5E2%2B5s%5E2t%2B19

P.S. Here is how it would look if we used long division:
         -19s^(4)t^3 - 3s^3t^2  + 5s^(2)t    + 19
         ______________________________________________  
3s^(2)t /-57s^(6)t^(4)-9s^5t^(3)+15s^(4)t^(2)+ 57s^(2)t
         -57s^(6)t^(4)
         ------------
                   0 - 9s^5t^(3)
                     - 9s^5t^3
                     ---------
                            0 + 15s^(4)t^(2)
                                15s^(4)t^(2)
                               -------------
                                          0 +57s^(2)t 
                                             57s^(2)t
                                             --------
                                                   0