(-x ^ { 5 } +2x ^ { 4 } -x ^ { 3 } +2x ^ { 2 } -x-1) \div (x-3)

asked by guest
on Mar 26, 2025 at 8:36 pm



You asked:

Evaluate the expression: −x5+2x4−x3+2x2−x−1x−3\frac{-{x}^{5} + 2 {x}^{4} - {x}^{3} + 2 {x}^{2} - x - 1}{x - 3}

MathBot Answer:

Evaluated



−x5+2x4−x3+2x2−x−1x−3=−x5+2x4−x3+2x2−x−1x−3\displaystyle \frac{-{x}^{5} + 2 {x}^{4} - {x}^{3} + 2 {x}^{2} - x - 1}{x - 3} = \frac{- x^{5} + 2 x^{4} - x^{3} + 2 x^{2} - x - 1}{x - 3}

Expanded

−x5+2x4−x3+2x2−x−1x−3=−x5x−3+2x4x−3−x3x−3+2x2x−3−xx−3−1x−3\frac{-{x}^{5} + 2 {x}^{4} - {x}^{3} + 2 {x}^{2} - x - 1}{x - 3} = - \frac{x^{5}}{x - 3} + \frac{2 x^{4}}{x - 3} - \frac{x^{3}}{x - 3} + \frac{2 x^{2}}{x - 3} - \frac{x}{x - 3} - \frac{1}{x - 3}

Factored

−x5+2x4−x3+2x2−x−1x−3=−(x−1)(x4−x3−2x−1)x−3\frac{-{x}^{5} + 2 {x}^{4} - {x}^{3} + 2 {x}^{2} - x - 1}{x - 3} = - \frac{\left(x - 1\right) \left(x^{4} - x^{3} - 2 x - 1\right)}{x - 3}

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