To find minimal polynomial of a linear transformation

Let $ V$ and $ W$ be finite dimensional vector spaces over $ \mathbb{R}$ and let $ T_{1} : V \rightarrow V$ and $ T_{2} : W \rightarrow W$ be linear transformations whose minimal polynomials are given by $ f_{1}(x)=x^{3}+x^{2}+1$ and $ f_{2}(x)=x^{4}-x{2}-2$ . Let $ T: V \bigoplus W \rightarrow V \bigoplus W$ be the linear transformation defined by $ T(v,w)=(T_{1}(v),T_{2}(w))$ for $ (v,w) \in V \bigoplus W$ and let $ f(x)$ be the minimal polynomial of $ T$ . Then, 1) deg$ f(x)=7$ 2)deg$ f(x)=5$ 3) nullity$ (T)=1$ 4)nullity$ (T)=0$ .