For a polynomial \(P(x)=ax^2+bx+c\), consider the following two kinds of transformations:
Swap coefficients \(a\) and \(c\). Hence the polynomial \(P(x)\) becomes \(cx^2+bx+a\) after this transformation.
For any number \(t\) of your choice, change the variable \(x\) into \(x+t\). For example, with the choice of \(t=1\), after this transformation, the polynomial \(x^2+x+1\) becomes \((x+1)^2+(x+1)+1=x^2+3x+3\).
Is it possible, using only a sequence of these two transformations, to change the polynomial \(x^2-x-2\) into the polynomial \(x^2-x-1\)?