We are asked to find the remainder when the polynomial $x^2 + 3x$ is divided by $x$.

1. Problem Description

We are asked to find the remainder when the polynomial $x^2 + 3x$ is divided by $x$.

2. Solution Steps

To find the remainder when $x^2 + 3x$ is divided by $x$, we can perform polynomial long division or simply factor out $x$ from the expression $x^2 + 3x$.

Factoring out $x$, we have:

$x^2 + 3x = x(x + 3)$

This means that $x^2 + 3x$ can be written as $x$ multiplied by $(x + 3)$. Since $x^2 + 3x = x(x+3) + 0$, the quotient is $x+3$ and the remainder is $0$.

Alternatively, we can perform polynomial long division.

x + 3

x | x^2 + 3x

- (x^2)

3x

- (3x)

0

The remainder is $0$.

3. Final Answer

0