$\displaystyle T:R_{3}[x]->R_{3}[x]$ is lenear transformation given by $\displaystyle A=(\begin{array}{ccc}

4 & 2 & 0\\

2 & 3 & 2\\

0 & 2 & 2\end{array})$with respect to $\displaystyle B=(1+x,1+x^{2},x+x^{2})$ basis

find ker T and ImT ?

How i tried to solve it:

$\displaystyle T(v_{1})=4(1+x)+2(1+x^{2})+0$

$\displaystyle T(v_{2})=5x^{2}+4x+5$

$\displaystyle T(v_{3})=2+2x+4x^{2}$

so i got the image of three vectors.

how to find the Im T and KerT