State the Zero Product Property in your own words. Provide an example.

If the product of two or more factors is zero, then at least one of the factors must be zero. Example: If (x-2)(x+3) = 0, then x-2=0 or x+3=0.

Solve the following quadratic equation by factoring: x² + 5x = 0. Show your work.

x(x+5) = 0, therefore x = 0 or x+5 = 0, so x = 0 or x = -5.

(x-4)(x+2) = 0, therefore x-4 = 0 or x+2 = 0, so x = 4 or x = -2.

I can solve quadratic equations by factoring and applying the zero product property.

1
The zero factor property states that if a × b = 0, then either a = 0 or b = 0 or both = 0.
2
When solving quadratic equations by factoring, the x-intercepts on the graph represent the values that make the equation equal to 0.
3
When factoring a quadratic equation in the form ax² + bx + c = 0 where a ≠ 1, techniques like grouping, trial and error, or the bottoms up method can be used.