The function f is defined by f(x) = (x-3)(x+7). What is the product of the zeros of f?

The zeros of $f(x) = (x - 3)(x + 7)$ are the values that make a factor zero: $x = 3$ and $x = -7$. Their product is $3 \times (-7) = -21$. As a check, expand: $f(x) = x^2 + 4x - 21$, and the product of the roots is the constant term, $-21$. A common wrong answer is 21, from dropping the negative sign, and another is $-4$, the sum of the zeros. A third is 10, the distance between the zeros. The question asks for the product, so multiply the two zeros together and keep the sign.