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Now, we can see that the factor pair (2, 6) satisfies our purpose as the sum of 6 and 2 is 8 and the product is 12. Split the middle term 8x in such a way that the factors of the product of 1 and 12 add up to make 8. We determine the factor pairs of the product of a and c such that their sum is equal to b. We split the middle term b of the quadratic equation ax 2 + bx + c = 0 when we try to factorize quadratic equations. The product of the roots in the quadratic equation ax 2 + bx + c = 0 is given by \(\alpha\beta\) = c/a.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).
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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. 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.