Solving by factoring

Japanese school year: Junior high 3

What you learn

You will learn how to solve quadratic equations by factoring expressions and setting each factor to zero. This technique is often used to solve geometric area problems and motion analysis efficiently. Mastering basic polynomial factoring formulas beforehand is essential for learning this method smoothly.

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Key points

This is the fundamental rule for solving quadratic equations by factoring. If the product of two factors $A$ and $B$ is 0, then $A = 0$ or $B = 0$ .

AB = 0 \iff A = 0 \lor B = 0

Use this to read the solutions directly from a factored equation. Making each factor equal to zero gives the solutions $x = \alpha$ and $x = \beta$ .

(x - \alpha)(x - \beta) = 0 \implies x = \alpha, \beta

This is an important rule when solving quadratic equations. Move all terms to one side to make it " $= 0$ ", and never divide both sides by $x$ to avoid losing the solution $x = 0$ .

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Practice 1Coming soon