If the product of two numbers equals 0, one of these numbers has to be equal to 0. This property does not work for numbers other than 0.
Explanation of the Error: See solution. Solutions to the Equation: x = -6 or x= 3
Practice makes perfect
Let's take a look at the Jamila's solution. We will check each pair of lines, one pair at a time. We want to make sure that, within each pair, the second statement follows from the first one. Let's take a look at the first pair.
x^2 + 3x-10 = 8
(x+5)(x-2) = 8
Within the first pair, there is no error. Now, let's take a look at the second pair.
(x+5)(x-2) = 8
x + 5 = 8 or x - 2 = 8
Notice that here, from the fact that the product of two numbers equals 8, Jamila concludes that one of these numbers has to be equal to 8. While such conclusion is valid if we had 0 on the right-hand side, it is not valid in general. In particular, it is not valid when we have 8 on the right-hand side. Let's fix the reasoning by making sure that we have 0 on the right-hand side before factoring.
By the Zero Product Property, if the product of two numbers equals 0, then one of these numbers equals 0. Therefore, we have the following two possibilities.
x + 6 = 0 or x - 3 = 0
Finally, let's find the solutions to the given equation.
x = -6 or x = 3
