Transforming into polynomials

Question

Transform this into a polynomial: $-x^2+6x-9$

Is there a formula?

What number $k^2$ can be a negative number?

I thought that only $-k ^{(odd number)}$ could be negative, but it is a binomial so...

Answer 1

Right, for any real number its square is never negative. However, a good trick when the $x^2$ term is negative is to factor out a $-1$. Here we now have $$-(x^2-6x+9).$$

Then, you simply factor $x^2-6x+9 = (x-3)^2$, so the answer becomes $-(x-3)^2$.

-FruDe