Zero-factor principle
The Zero-Factor Principle states that if the product of two numbers equals zero, then at least one of those numbers must be zero (if AB = 0, then A = 0 or B = 0). Taught in Yoshiwara Elementary Algebra Chapter 6: Quadratic Equations, this principle is the key to solving factored quadratic equations for Grade 6 students. By factoring a quadratic and applying the zero-factor principle to each factor, students find all solutions efficiently.
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 $(x 7)(x + 2) = 0$, we set each factor to zero. This gives us $x 7 = 0$ or $x + 2 = 0$, so the solutions are $x = 7$ and $x = 2$. If $y(y 10) = 0$, then either $y = 0$ or $y 10 = 0$. The two solutions for the equation are $y = 0$ and $y = 10$. Given $(2a + 1)(a 5) = 0$, we solve $2a + 1 = 0$ to get $a = \frac{1}{2}$, and we solve $a 5 = 0$ to get $a = 5$.
Common Questions
What is the zero-factor principle?
It states that if a product equals zero, then at least one factor must be zero. If AB = 0, then A = 0 or B = 0.
How do you use the zero-factor principle to solve equations?
Factor the equation to get a product equal to zero, then set each factor equal to zero separately and solve. For example, (x - 3)(x + 2) = 0 gives x = 3 or x = -2.
Why does the equation need to equal zero?
The zero-factor principle only works when the product is zero. If the product equals a non-zero number, you cannot directly set each factor equal to that number.
Where is the zero-factor principle in Yoshiwara Elementary Algebra?
It is covered in Chapter 6: Quadratic Equations of Yoshiwara Elementary Algebra.
Can the zero-factor principle find more than two solutions?
Yes. If there are three or more factors, set each one equal to zero to find all possible solutions.