Question about surjectivity of a linear map

Question

Why is the following linear map not surjective?

$T \in \mathcal L (\mathcal P(\mathbb R),\mathcal P(\mathbb R)): (Tp)(x) = x^2p(x)$

According to my book, $1$ is not in the range of $T$. Can't you get $1$ for $p(x) = x$ and $x = 1$, so $x^2p(x) = 1^2\cdot1$? What am I misunderstanding?

Thank you.

Answer 1

For p(x) = x, you get T(p(x)) = x^2, and this is not constant polynomial q(x) = 1, what you are getting is the value 1 at x = 1.