Find the number of terms in the quotient of following division of algebraic expressions .

$\frac{x^3+2x^2+3x}{2x}$

$\frac{{\mathrm{x}}^3+2{\mathrm{x}}^2+3\mathrm{x}}{2\mathrm{x}}=\frac{{\mathrm{x}}^3}{2\mathrm{x}}+\frac{2{\mathrm{x}}^2}{2\mathrm{x}}+\frac{3\mathrm{x}}{2\mathrm{x}}$ 

$=\frac{\mathrm{x}\times \mathrm{x}\times \mathrm{x}}{2\times \mathrm{x}}+\frac{2\times \mathrm{x}\times \mathrm{x}}{2\times \mathrm{x}}+\frac{3\times \mathrm{x}}{2\times \mathrm{x}}$

$=\frac{\mathrm{x}\times \mathrm{x}\times \cancel{\mathrm{x}}}{2\times \cancel{\mathrm{x}}}+\frac{\cancel{2}\times \mathrm{x}\times \cancel{\mathrm{x}}}{\cancel{2}\times \cancel{\mathrm{x}}}+\frac{3\times \cancel{\mathrm{x}}}{2\times \cancel{\mathrm{x}}}$

$=\frac{{\mathrm{x}}^2}{2\mathrm{x}}+\mathrm{x}+\frac{3}{2}$

When we performed the given division, we clearly got a trinomial as the answer.

So, the number of terms are 3.