SOLUTION: x^3+x^2 x+4 ------- . ----------- - x^2-16 3x^4+x^3-2x^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: x^3+x^2 x+4 ------- . ----------- - x^2-16 3x^4+x^3-2x^2      Log On


   

Question 144441: x^3+x^2 x+4
------- . -------------
x^2-16 3x^4+x^3-2x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%5E3%2Bx%5E2%29%2F%28x%5E2-16%29%29%28%28x%2B4%29%2F%283x%5E4%2Bx%5E3-2x%5E2%29%29 Start with the given expression

%28%28x%5E2%28x%2B1%29%29%2F%28x%5E2-16%29%29%28%28x%2B4%29%2F%283x%5E4%2Bx%5E3-2x%5E2%29%29 Factor x%5E3%2Bx%5E2 to get x%5E2%28x%2B1%29

Factor x%5E2-16 to get %28x%2B4%29%28x-4%29

Factor 3x%5E4%2Bx%5E3-2x%5E2 to get x%5E2%28x%2B1%29%283x-2%29


%28x%5E2%28x%2B1%29%28x%2B4%29%29%2F%28%28x%2B4%29%28x-4%29x%5E2%28x%2B1%29%283x-2%29%29 Combine the fractions


Cancel like terms


1%2F%28%28x-4%29%283x-2%29%29 Simplify



So %28%28x%5E3%2Bx%5E2%29%2F%28x%5E2-16%29%29%28%28x%2B4%29%2F%283x%5E4%2Bx%5E3-2x%5E2%29%29 simplifies to 1%2F%28%28x-4%29%283x-2%29%29. In other words, where x%3C%3E-4, x%3C%3E-1 , or x%3C%3E0