$(−8 + 𝑥^5 − 3𝑥^4 + 2𝑥^2)$ / $(3𝑥^4 − 2𝑥^3 + 5𝑥^2 − 𝑥 + 7)$

asked by guest
on Jan 27, 2025 at 3:11 pm



You asked:

Evaluate the expression: \(\frac{-8 + {x}^{5} - 3 {x}^{4} + 2 {x}^{2}}{3 {x}^{4} - 2 {x}^{3} + 5 {x}^{2} - x + 7}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{-8 + {x}^{5} - 3 {x}^{4} + 2 {x}^{2}}{3 {x}^{4} - 2 {x}^{3} + 5 {x}^{2} - x + 7} = \frac{x^{5} - 3 x^{4} + 2 x^{2} - 8}{3 x^{4} - 2 x^{3} + 5 x^{2} - x + 7} \)

Expanded

\[\frac{-8 + {x}^{5} - 3 {x}^{4} + 2 {x}^{2}}{3 {x}^{4} - 2 {x}^{3} + 5 {x}^{2} - x + 7} = \frac{x^{5}}{3 x^{4} - 2 x^{3} + 5 x^{2} - x + 7} - \frac{3 x^{4}}{3 x^{4} - 2 x^{3} + 5 x^{2} - x + 7} + \frac{2 x^{2}}{3 x^{4} - 2 x^{3} + 5 x^{2} - x + 7} - \frac{8}{3 x^{4} - 2 x^{3} + 5 x^{2} - x + 7}\]

Factored

\[\frac{-8 + {x}^{5} - 3 {x}^{4} + 2 {x}^{2}}{3 {x}^{4} - 2 {x}^{3} + 5 {x}^{2} - x + 7} = \frac{\left(x^{2} - 2 x + 2\right) \left(x^{3} - x^{2} - 4 x - 4\right)}{3 x^{4} - 2 x^{3} + 5 x^{2} - x + 7}\]

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