(2x^5 + x^4 - 3x^3 + x^2)/(x^3 - x + 1)
You asked:
Evaluate the expression: \(\frac{2 {x}^{5} + {x}^{4} - 3 {x}^{3} + {x}^{2}}{{x}^{3} - x + 1}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{2 {x}^{5} + {x}^{4} - 3 {x}^{3} + {x}^{2}}{{x}^{3} - x + 1} = \frac{2 x^{5} + x^{4} - 3 x^{3} + x^{2}}{x^{3} - x + 1} \)
Expanded
\[\frac{2 {x}^{5} + {x}^{4} - 3 {x}^{3} + {x}^{2}}{{x}^{3} - x + 1} = \frac{2 x^{5}}{x^{3} - x + 1} + \frac{x^{4}}{x^{3} - x + 1} - \frac{3 x^{3}}{x^{3} - x + 1} + \frac{x^{2}}{x^{3} - x + 1}\]
Factored
\[\frac{2 {x}^{5} + {x}^{4} - 3 {x}^{3} + {x}^{2}}{{x}^{3} - x + 1} = \frac{x^{2} \cdot \left(2 x - 1\right) \left(x^{2} + x - 1\right)}{x^{3} - x + 1}\]