Q:

# How do you solve quadratic equations by factoring?

A:

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.

## Keep Learning

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.

Sources:

## Related Questions

• A: According to Wolfram|Alpha, there are various mathematical equations that produce a graph in the shape of a heart. A simple example is the following equati... Full Answer >
Filed Under:
• A: An inequality graph is a graph on which every point within the region plotted is a solution to the inequality. A linear inequality includes everything on o... Full Answer >
Filed Under:
• A: To find the slope of the tangent line to the graph of a function at a point, find the derivative of the function, then plug in the x-value of the point. Co... Full Answer >
Filed Under:
• A: X3y3 + z3 can be factored by using a graphing calculator or through factoring as a sum of cubes. The final answer for factoring x3y3 + z3 is (xy + z) times... Full Answer >
Filed Under:
PEOPLE SEARCH FOR