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To determine which factors to use, we must also determine the sum of the factors. There are many ways 12 can be factored, such as using -12 and -1 or using 6 and 2. To factor the expression x^2+7x+12, we must first determine the factors of c, in this case 12. Now, let’s solve for the x-intercepts by factoring. To start, let’s try solving the equation: But no need to worry, we include more complex examples in the next section. We simply must determine the values of r_1 and r_2. In these cases, solving quadratic equations by factoring is a bit simpler because we know factored form, y=(x-r_1)(x-r_2), will also have no coefficients in front of x. If a=1, then no coefficient appears in front of x^2. Remember, the standard form of a quadratic is:įor more information about forms of quadratics, check out our article on the different forms of quadratics.
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For our purpose, a simple quadratic means a quadratic where a=1. The x-intercepts can also be referred to as zeros, roots, or solutions. When you are asked to “solve a quadratic equation”, you are determining the x-intercepts. Return to the Table of Contents Factoring Quadratic Equations Examplesīefore things get too complicated, let’s begin by solving a simple quadratic equation. …we are simply saying that when we multiply (x-r_1) and (x-r_2), we will get the product ax^2+bx+x. Likewise, when we factor the standard from of a quadratic equation:
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Video Examples of Factoring Quadratic Equation.Solving Quadratic Equations with the “AC Method”.