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