The zeroes of the polynomial $x^2 + 5x + 6$ are :

Step 1: Set the polynomial to zero

To find the zeroes of a polynomial, we set the polynomial equal to zero. This gives us a quadratic equation that we need to solve for $x$.

Step 2: Factor the quadratic equation

We need to find two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of the $x$ term). These numbers are 2 and 3. So, we can factor the quadratic equation as $(x+2)(x+3)=0$.

Step 3: Solve for x

For the product of two factors to be zero, at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for $x$. This gives us the two zeroes of the polynomial.

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