Solve t^5-8t^4+t^3-8t^2

$$t ^ { 5 } - 8 t ^ { 4 } + t ^ { 3 } - 8 t ^ { 2 }$$

Factor

$$\left(t-8\right)t^{2}\left(t^{2}+1\right)$$

Solution Steps

Factor out t^{2}.

$$t^{2}\left(t^{3}-8t^{2}+t-8\right)$$

Consider t^{3}-8t^{2}+t-8. Do the grouping t^{3}-8t^{2}+t-8=\left(t^{3}-8t^{2}\right)+\left(t-8\right), and factor out t^{2} in t^{3}-8t^{2}.

$$t^{2}\left(t-8\right)+t-8$$

Factor out common term t-8 by using distributive property.

$$\left(t-8\right)\left(t^{2}+1\right)$$

Rewrite the complete factored expression. Polynomial t^{2}+1 is not factored since it does not have any rational roots.

$$t^{2}\left(t-8\right)\left(t^{2}+1\right)$$

Evaluate

$$\left(t-8\right)t^{2}\left(t^{2}+1\right)$$