The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. In other words, if \( a \cdot b = 0 \), then either \( a = 0 \) or \( b = 0 \) (or both).
Quick Check Steps:
- Identify the equation: Ensure you have an equation of the form \( (factor_1) \cdot (factor_2) = 0 \).
- Set each factor to zero: Solve for each factor separately:
- \( factor_1 = 0 \)
- \( factor_2 = 0 \)
- Find solutions: The solutions to these equations are the values of the variable that make the original product zero.
Example:
If you have the equation: \[ (x - 3)(x + 2) = 0 \] Step 1: Identify the factors: \( x - 3 \) and \( x + 2 \).
Step 2: Set each factor to zero:
- \( x - 3 = 0 \) → \( x = 3 \)
- \( x + 2 = 0 \) → \( x = -2 \)
Step 3: Solutions are \( x = 3 \) and \( x = -2 \).
Summary:
Whenever you have an equation where two or more factors multiply to zero, you can use the Zero Product Property to find the solutions quickly.
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