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Math / Algebra / Grade 9 / ml901

Solve Quadratics by Factoring

Use factors and the zero-product rule to find both solutions.

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For x^2 + bx + c, find two numbers whose sum is b and product is c. Factor into two binomials. If their product is zero, at least one factor equals zero; solve each factor separately.

Worked example

x^2 - 7x + 12 = (x - 3)(x - 4). Setting each factor to zero gives x = 3 or x = 4. Substitution verifies both solutions.

1. Solve x^2 - 5x + 6 = 0.
2. Solve x^2 + 5x + 6 = 0.
3. Solve x^2 - 9 = 0.
4. Solve x^2 - 4x = 0.
5. Solve x^2 + 6x + 9 = 0.