What are the zeros of the polynomial $y=x^{2}+3 x ?$

Step 1 ：The zeros of a polynomial are the values of x for which the polynomial equals zero. In other words, they are the solutions to the equation \(y=0\). So, to find the zeros of the polynomial \(y=x^{2}+3 x\), we need to solve the equation \(x^{2}+3 x=0\).

Step 2 ：This is a quadratic equation, and we can solve it by factoring, completing the square, or using the quadratic formula. In this case, factoring seems to be the simplest method.

Step 3 ：We can factor out an x from each term to get \(x(x+3)=0\). Now, we can set each factor equal to zero and solve for x to find the zeros of the polynomial.

Step 4 ：The zeros of the polynomial are the solutions to the equation \(x^{2}+3 x=0\), which are x = -3 and x = 0. These are the values of x for which the polynomial equals zero.

Step 5 ：Final Answer: The zeros of the polynomial \(y=x^{2}+3 x\) are \(\boxed{-3}\) and \(\boxed{0}\).