Find the product:

By horizontal method:

$\left(x^{2}-3 x+7\right) \times(2 x+3)$

$=2 x\left(x^{2}-3 x+7\right)+3\left(x^{2}-3 x+7\right)$

$=2 x^{3}-6 x^{2}+14 x+3 x^{2}-9 x+21$

$=2 x^{3}-3 x^{2}+5 x+21$