The sum of the roots of the quadratic equation ax 2 + bx + c = 0 is given by \(\alpha + \beta\) = -b/a.Splitting the Middle Term for Factoring Quadratics Thus 3x 2 + 6x = 0 is factorized as 3x(x + 2) = 0.The algebraic common factor is x in both terms.The numerical factor is 3 (coefficient of x 2) in both terms.Let us solve an example to understand the factoring quadratic equations by taking the GCD out.Ĭonsider this quadratic equation: 3x 2 + 6x = 0 Using Algebraic Identities (Completing the Squares)įactoring Quadratics by Taking Out The GCDįactoring quadratics can be done by finding the common numeric factor and the algebraic factors shared by the terms in the quadratic equation and then take them out.There are different methods that can be used for factoring quadratic equations. Thus the equation has 2 factors (x+3) and (x-3)įactoring quadratics gives us the roots of the quadratic equation. Verify by substituting the roots in the given equation and check if the value equals 0. Thus the equation has 2 factors (x + 3) and (x + 2)ģ and -3 are the two roots of the equation. Consider the quadratic equation x 2 + 5x + 6 = 0 Let us go through some examples of factoring quadratics:ġ. Hence, factoring quadratics is a method of expressing the quadratic equations as a product of its linear factors, that is, f(x) = (x - \(\alpha\))(x - \(\beta\)). Thus, (x - \(\beta\)) should be a factor of f(x). Similarly, if x = \(\beta\) is the second root of f(x) = 0, then x = \(\beta\) is a zero of f(x). Thus, (x - \(\alpha\)) should be a factor of f(x). This means that x = \(\alpha\) is a zero of the quadratic expression f(x). Suppose that x = \(\alpha\) is one root of this equation.
Consider a quadratic equation f(x) = 0, where f(x) is a polynomial of degree 2. They are the zeros of the quadratic equation. Every quadratic equation has two roots, say \(\alpha\) and \(\beta\). The factor theorem relates the linear factors and the zeros of any polynomial. Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc. This method is also is called the method of factorization of quadratic equations.
So, either one or both of the terms are 0 i.e.Factoring quadratics is a method of expressing the quadratic equation ax 2 + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax 2 + bx + c = 0. We know that any number multiplied by 0 gets 0. We have two factors when multiplied together gets 0. We find that the two terms have x in common. We can factorize quadratic equations by looking for values that are common. If the coefficient of x 2 is greater than 1 then you may want to consider using the Quadratic formula. This is still manageable if the coefficient of x 2 is 1. In other cases, you will have to try out different possibilities to get the right factors for quadratic equations. In some cases, recognizing some common patterns in the equation will help you to factorize the quadratic equation.įor example, the quadratic equation could be a Perfect Square Trinomial (Square of a Sum or Square of a Difference) or Difference of Two Squares. Sometimes, the first step is to factor out the greatest common factor before applying other factoring techniques. The simplest way to factoring quadratic equations would be to find common factors. Solving Quadratic Equations using the Quadratic Formula Factoring Quadratic Equations (Square of a sum, Square of a difference, Difference of 2 squaresįactoring Quadratic Equations where the coefficient of x 2 is greater than 1įactoring Quadratic Equations by Completing the Square
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