Worked example
x² − 7x + 12 = 0
- Find two numbers with product 12 and sum −7: −3 and −4.
- Factor: (x − 3)(x − 4) = 0.
- Use the zero-product property: x = 3 or x = 4.
- Substitution verifies both roots.
Math guide
Factor when the number pattern is visible.
Factor a quadratic, apply the zero-product property, and verify that every root satisfies the original equation.
After moving every term to one side, express the quadratic as a product. If the product equals zero, at least one factor must be zero. Solve each factor and check both roots.
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