Question

Zero product property quick check

Answer 1

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:**
1. **Identify the equation:** Ensure you have an equation of the form \( (factor_1) \cdot (factor_2) = 0 \).
2. **Set each factor to zero:** Solve for each factor separately:
- \( factor_1 = 0 \)
- \( factor_2 = 0 \)
3. **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:
1. \( x - 3 = 0 \) → \( x = 3 \)
2. \( x + 2 = 0 \) → \( x = -2 \)

**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.