How Do You Solve Quadratic Equations by Factoring?

How Do You Solve Quadratic Equations by Factoring?

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.

  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.