I was reading this inequality question. Here is part of the text that I have question about:
$$2t^8-t^7-8t^6+t^5+15t^4-4t^3-11t^2+4t+4>0.$$ Using Maple, I got $$(2t^2-t-2)(t^2-t-1)(t^4+t^3-t^2-t+2)>0.$$
And by factoring we can solve the inequality. but I wonder is it possible to factor the polynomial $$2t^8-t^7-8t^6+t^5+15t^4-4t^3-11t^2+4t+4$$ By hand without using any math software? By the result of the factoring we can see the roots of polynomial are $\frac{1\pm\sqrt{17}}{4}$ and $\frac{1\pm\sqrt5}{2}$, So we couldn't guess a number for example an integer like $a$ and see it makes the equation zero to have the factor $t-a$, also I can't see any obvious way to factor the polynomial so I wonder how we can factor it by hand.