factorize t^4-2t^3+4t-1
You asked:
Factor the expression: \(\displaystyle {t}^{4} - 2 {t}^{3} + 4 t - 1\)
MathBot Answer:
Factorization over the real numbers:
\[\left(t + \left(- \frac{1}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 2 + \frac{6}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 1 + 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}}}}}{2} + \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 1 + 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}}}{2}\right)\right) \left(t - \left(\frac{1}{2} + \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 1 + 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}}}{2} + \frac{\sqrt{- \frac{6}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 1 + 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}}} - 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 2}}{2}\right)\right) \left(t - \left(\frac{1}{2} + \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 1 + 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}}}{2} - \frac{\sqrt{- \frac{6}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 1 + 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}}} - 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 2}}{2}\right)\right) \left(t - \left(- \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 1 + 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}}}{2} + \frac{1}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 2 + \frac{6}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}} + 1 + 2 \sqrt[3]{\frac{\sqrt{681}}{36} + \frac{3}{4}}}}}}{2}\right)\right)\]