SAT Math: Solving Quadratic Equations by Factoring
45+ practice questions in Praczo
The concept, explained
- 1
The Zero Product Property: if ab = 0, then a = 0 or b = 0. This is the core idea — get one side equal to zero, factor, then set each factor to zero.
- 2
Always move everything to one side first so the equation equals zero before factoring. Never factor with non-zero values on both sides.
- 3
After factoring, write two equations (factor₁ = 0 and factor₂ = 0) and solve each. You'll get two solutions, sometimes the same (a double root).
- 4
The solutions are the x-intercepts of the corresponding parabola.
- 5
When the SAT gives a factored form like (x − 3)(x + 5) = 0, read the solutions directly: x = 3 and x = −5.
- ✗ Getting the wrong sign: (x + 5) = 0 gives x = −5, not x = 5. The solution is the value that makes the factor zero.
- ✗ Not moving all terms to one side first: trying to factor x² + 2x = 15 without rewriting as x² + 2x − 15 = 0.
SAT-style practice
What are the solutions to x² + 2x − 15 = 0?
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