Expand $Q$ to prove that the polynomials $P$ and $Q$ are the same.
$$\begin{array}{l}{P(x)=3 x^{4}-5 x^{3}+x^{2}-3 x+5} \\ {Q(x)=(((3 x-5) x+1) x-3) x+5}\end{array}$$
Try to evaluate $P(2)$ and $Q(2)$ in your head, using the forms given. Which is easier? Now write the polynomial $R(x)=x^{5}-2 x^{4}+3 x^{3}-2 x^{2}+3 x+4$ in "nested" form, like the polynomial $Q .$ Use the nested form to find $R(3)$ in your head.
Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?