How do you solve quadratic equations by factoring?


Quick Answer

To solve quadratic equations by factoring, it's a matter of finding the x-intercepts of the graph, or the point at which the graph crosses the x-axis. Quadratics are in the form of ax^2 + bx + c = 0, so you have to simplify the equation into simple binomials.

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Full Answer

  1. Convert the equation into standard form if necessary

    Converting the equation makes it easier to factor into two binomials. Quadratic equations are parabolas that cross the x-axis up to two times. For an example, use the quadratic equation x^2 - 5x - 6 = 0.

  2. Separate the polynomial into two binomials

    Ask yourself what factors of -6 add up to -5. Binomials are multiplied by the FOIL method of combining terms, and the two middle terms are added. In the example, the relevant factors are 1 and -6. When factored, the equation is (x +1)(x-6) = 0. If either binomial is zero, it satisfies the equation.

  3. Express the zeros as both terms

    The zeros of the example equation are -1 and 6. Note that not all quadratic equations can factor into real numbers and thus are not solvable by this method. These equations do not touch the x-axis and have no real solutions.

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