Question

F(x) = x2+3x+2 x2+5x+4 Why is there no zero at x = –1?

Answer 1

You could rewrite $F(x)$ as

$\dfrac{x^2+3x+2}{x^2+5x+4}=\dfrac{(x+1)(x+2)}{(x+1)(x+4)}$

and be tempted to cancel out the factors of $x+1$. But this cancellation is only valid when $x\neq-1$.

When $x=-1$, you end up with the indeterminate form $\dfrac00$, which is why $-1$ is not a zero.