We need to factorize:
We can, by the rational root theorem, see that there are no roots of this polynomial.Next observation is that $64=(8)^2$. So this means that if the first part of the polynomial is a square,we can rewrite the whole polynomial as the difference of two squares.But it turns out that the first part of the polynomial is not a square. However,we can note that,
Therefore,letting $(x^2)-8x+7=p$,we can rewrite the given polynomial as
which I thought would be factorizable, but I seem to be wrong. So how can I factorize this polynomial? I would appreciate a small hint.
EDIT: The original polynomial seems to have been
But there is no point in changing the whole question.To factorize this polynomial,we would do the exact same things as before and find that