Find the value of the given expression (x3+2x2+3x)÷2x

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Question

Find the value of the given expression
$(x^{3} + 2 x^{2} + 3 x) \div 2 x$

Options:

A .

\frac{(x^{2} + 2 x + 3)}{2}

B .

\frac{1}{2}

C . (

x^{2} + 2 x + 3)

D . 1

Answer: Option A
:
A

Divide all the terms of the expression $(x^{3} + 2 x^{2} + 3 x)$ separately by $2 x$ .
$\frac{x^{3}}{2 x} = \frac{x^{2}}{2}$ ;
$\frac{2 x^{2}}{2 x} = x$ ;
$\frac{3 x}{2 x} = \frac{3}{2}$ .
Therefore, $\frac{(x^{3} + 2 x^{2} + 3 x)}{2 x} = \frac{x^{2}}{2} + x + \frac{3}{2} = \frac{(x^{2} + 2 x + 3)}{2}$

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