<s>[INST] Factoring the following polynomials 
Factorize the following polynomial:

*

*$t^3 -9t +8$

*$t^6 -91t^2 +90$

 [/INST] It's not so bad to be baffled... :) 
Putting $t=1$ and and $t^2=1$ into the first and second expressions respectively will make them zero, so $(t-1)$ and $(t^2-1)$ are factors for the first and second expressions respectively. 
You can work out the other factor(s) by equating coefficients of powers of $t$. 
$$\begin{align}t^3-9t+8&=(t-1)(t^2+t-8)\\ \\
t^6-91t^2+90&=(t^2-1)(t^4+t^2-90)\\
&=\left[(t-1)(t+1)\right]\left[(t^2-9)(t^2+10)\right]\\
&=(t-1)(t+1)(t-3)(t+3)(t^2+10)\\
&=(t-3)(t-1)(t+3)(t+3)(t^2+10)\\\end{align}$$
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