The zero-factor principle
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces the zero-factor principle, also known as the zero product property. It states that if the product of two factors is zero, then at least one of the factors must be zero. This principle is the foundation for solving quadratic equations by factoring.
Key Concepts
Property If the product of two numbers is zero, then one (or both) of the numbers must be zero. Using symbols,.
If $AB = 0$, then either $A = 0$ or $B = 0$.
Examples To solve $(x 7)(x + 3) = 0$, set each factor to zero. $x 7 = 0$ gives $x = 7$, and $x + 3 = 0$ gives $x = 3$.
Common Questions
What is the zero-factor principle?
The zero-factor principle states that if A × B = 0, then A = 0 or B = 0 (or both). This is also called the zero product property.
How is the zero-factor principle used to solve equations?
Factor the equation so the product equals zero, then set each factor equal to zero and solve. For example, (x - 2)(x + 3) = 0 gives x = 2 or x = -3.
Why must at least one factor be zero when their product is zero?
Zero times any number is zero. So if a product is zero, one or both of the factors must be zero.
Can the zero-factor principle be used for expressions with three or more factors?
Yes. If a product of multiple factors equals zero, at least one of them must be zero.
Where is the zero-factor principle taught?
The zero-factor principle is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.