Null space and range

Consider the set $P$ of all polynomials of degree at most $2$:

$$P = \{ a x^2 +bx +c: a, b,c \in \mathbb{R} \}$$You can easily prove that this set is a vector space with the following sum and product by a scalar. If $p(x)= a_1 x^2 + b_1 x + c_1$ and $q(x)= a_2 x^2 + b_2 x + c_2$ are in $P$, then:$$p(x) + q(x) = (a_1 +a_2)x^2 + (b_1+b_2)x + c_1 +c_2$$$$\lambda p(x) = (\lambda a_1) x^2 + (\lambda b_1)x + \lambda c_1$$

Let us say that $T: \, P\rightarrow P$ is given by $$T(p(x)) = 5 \, p(x)$$
Determine the null space of $T$