Solving by Factoring

Solving by Factoring

If a quadratic can be factored into $(x + p)(x + q) = 0$, then the solutions are $x = -p$ or $x = -q$.

Method

1. Write the equation in standard form: $ax^2 + bx + c = 0$
2. Find two numbers that multiply to c and add to b
3. Factor and set each factor to zero
4. Solve each simple equation

Example

Solve $x^2 - 5x + 6 = 0$

Find two numbers that multiply to 6 and add to -5: those are -2 and -3.

$(x - 2)(x - 3) = 0$

So $x = 2$ or $x = 3$