#### Answer

$$T_{3}(x)=9+8(x-3)+2(x-3)^{2}+2(x-3)^{3}$$

#### Work Step by Step

In general, with $a=3$
$$
T_{3}(x)=f(3)+f^{\prime}(3)(x-3)+\frac{f^{\prime \prime}(3)}{2}(x-3)^{2}+\frac{f^{\prime \prime \prime}(3)}{6}(x-3)^{3}
$$
Using the information provided, we find
$$
T_{3}(x)=9+8(x-3)+2(x-3)^{2}+2(x-3)^{3}
$$