solving quadratic equations by factoring

SOLVING QUADRATIC EQUATIONS BY FACTORING HOW TO

Note that the quadratic formula technique can easily find irrational and imaginary roots, unlike the factoring method. You can also write the answers as, the result of multiplying the numerators and denominators of both by −1.

The coefficients for the quadratic formula are a = −4, b = 6, and c = −1: You should memorize the quadratic formula if you haven't done so already. A word of warning: Make sure that the quadratic equation you are trying to solve is set equal to 0 before plugging the quadratic equation's coefficients a, b, and c into the formula. This method is especially useful if the quadratic equation is not factorable. If an equation can be written in the form ax 2 + bx + c = 0, then the solutions to that equation can be found using the quadratic formula: Plug each answer into the original equation to ensure that it makes the equation true.Īdd 13 x 2and −10 x to both sides of the equation:įactor the polynomial, set each factor equal to 0, and solve.īecause all three of these x‐values make the quadratic equation true, they are all solutions. Set each factor equal to 0 and solve the smaller equations.Ĥ. Move all non‐zero terms to the left side of the equation, effectively setting the polynomial equal to 0.ģ. To solve a quadratic equation by factoring, follow these steps:ġ.

SOLVING QUADRATIC EQUATIONS BY FACTORING HOW TO

Of those two, the quadratic formula is the easier, but you should still learn how to complete the square.

The other two methods, the quadratic formula and completing the square, will both work flawlessly every time, for every quadratic equation. The easiest, factoring, will work only if all solutions are rational. There are three major techniques for solving quadratic equations (equations formed by polynomials of degree 2).

Solving quadratic equations by factoring