To apply the zero product rule, one side of the
equation must be equal to and the other side
must be written in factored form.

The zero product rule is a game-changer when it comes to solving quadratic equations and can be traced back to ancient times when mathematicians first started exploring the relationships between polynomials and their roots. This rule states that if the product of two factors equals zero, then at least one of the factors must be zero. It’s like a magical key to unlock the possible solutions of an equation!

In real-world application, the zero product rule pops up in various fields, especially in physics and engineering. For instance, if you’re modeling the trajectory of a ball, the equation you derive might lead you to apply the zero product rule to find out when the ball will hit the ground (i.e., when its height equals zero). By factoring the height equation, you determine impactful moments during its flight.