Question

How do you solve (x – 7)(x + 2) = 0 using the zero product property?

Answer 1

We will first assume that a = x – 7 and b = x + 2 and then we will use the zero product property on a.b = 0 to get a = 0 or b = 0 or both equal zero.

Complete step-by-step answer:
We are given that we are required to solve (x – 7)(x + 2) = 0 using the zero product property.
Let us assume that a = x – 7 and b = x + 2, then we can write the given expression as a . b
Now, we know that if a.b = 0, then either a = 0, b = 0 or both a and b equals 0.
Using this, we get either x – 7 = 0 or x + 2 = 0 or both of these are true.
This implies that either x = 7 (we took the 7 from subtraction in the left hand side to addition with 0 on the right hand side) or x = - 2 (we took the 2 from addition in the left hand side to subtraction with 0 on the right hand side) or both are true at the same time.
Since we know that if x = 7, then x cannot be equal to – 2 and vice versa that if x is equal to – 2, then x cannot be equal to 7.
Therefore, we have either x = 7 or x = - 2.

Hence, the answer is either x = 7 or x = - 2.

Note:
The students must know the definition of the zero product property.
Zero Product Property: The zero product property states that if a.b = 0 for some real numbers a and b, then either a = 0 or b = 0 or both are equal to 0.
The students must notice that in the given question we discarded the possibility of both being zero at the same time with a valid reason.