State true or false $x=\Theta(n^4)$, $y=\Theta(n^2)$ therefore $x/y=\Theta(n^2)$
I think the ans is true,but in the book it says false. What is the explanation?
My reason for thinking it to be true is that say for x we have a polynomial $n^4$+...... and for y we have a polynomial like $n^2$+... so if we divide x/y the ans should have the highest power of $n^2$ and the resultant polynomial will be like $n^2$+.... So it should be $\Theta(n^2)$